Section 5-7Diagonals and Angles of Polygons

Wed, Feb 02

Essential Questions

✤ How are polygons classified according to their sides?

✤ How do you find the sum of the angle measures of polygons?

✤ Where you’ll see this:

✤ Safety, hobbies, nature

Wed, Feb 02

Vocabulary

1. Polygon:

2. Side:

3. Vertex:

4. Convex:

5. Concave:

6. Regular Polygon:

7. Diagonal:

Wed, Feb 02

Vocabulary

1. Polygon: A closed figure made by joining three or more segments at their endpoints

2. Side:

3. Vertex:

4. Convex:

5. Concave:

6. Regular Polygon:

7. Diagonal:

Wed, Feb 02

Vocabulary

1. Polygon: A closed figure made by joining three or more segments at their endpoints

2. Side: One of the segments that makes up the polygon

3. Vertex:

4. Convex:

5. Concave:

6. Regular Polygon:

7. Diagonal:

Wed, Feb 02

Vocabulary

1. Polygon: A closed figure made by joining three or more segments at their endpoints

2. Side: One of the segments that makes up the polygon

3. Vertex: The point where segments meet

4. Convex:

5. Concave:

6. Regular Polygon:

7. Diagonal:

Wed, Feb 02

Vocabulary

1. Polygon: A closed figure made by joining three or more segments at their endpoints

2. Side: One of the segments that makes up the polygon

3. Vertex: The point where segments meet

4. Convex: When there are no indentations in a polygon

5. Concave:

6. Regular Polygon:

7. Diagonal:

Wed, Feb 02

Vocabulary

1. Polygon: A closed figure made by joining three or more segments at their endpoints

2. Side: One of the segments that makes up the polygon

3. Vertex: The point where segments meet

4. Convex: When there are no indentations in a polygon

5. Concave: When there is an indentation into a polygon

6. Regular Polygon:

7. Diagonal:

Wed, Feb 02

Vocabulary

1. Polygon: A closed figure made by joining three or more segments at their endpoints

2. Side: One of the segments that makes up the polygon

3. Vertex: The point where segments meet

4. Convex: When there are no indentations in a polygon

5. Concave: When there is an indentation into a polygon

6. Regular Polygon: A polygon where all the sides and angles are congruent

7. Diagonal:

Wed, Feb 02

Vocabulary

1. Polygon: A closed figure made by joining three or more segments at their endpoints

2. Side: One of the segments that makes up the polygon

3. Vertex: The point where segments meet

4. Convex: When there are no indentations in a polygon

5. Concave: When there is an indentation into a polygon

6. Regular Polygon: A polygon where all the sides and angles are congruent

7. Diagonal: A segment that joins two vertices but is not a side

Wed, Feb 02

Polygons and Their Sides

5 sides: 6 sides: 7 sides:

9 sides:8 sides: 10 sides:

Wed, Feb 02

Polygons and Their Sides

5 sides: 6 sides: 7 sides:

9 sides:8 sides: 10 sides:

Pentagon

Wed, Feb 02

Polygons and Their Sides

5 sides: 6 sides: 7 sides:

9 sides:8 sides: 10 sides:

Pentagon

Wed, Feb 02

Polygons and Their Sides

5 sides: 6 sides: 7 sides:

9 sides:8 sides: 10 sides:

Pentagon Hexagon

Wed, Feb 02

Polygons and Their Sides

5 sides: 6 sides: 7 sides:

9 sides:8 sides: 10 sides:

Pentagon Hexagon

Wed, Feb 02

Polygons and Their Sides

5 sides: 6 sides: 7 sides:

9 sides:8 sides: 10 sides:

Pentagon Hexagon Heptagon

Wed, Feb 02

Polygons and Their Sides

5 sides: 6 sides: 7 sides:

9 sides:8 sides: 10 sides:

Pentagon Hexagon Heptagon

Wed, Feb 02

Polygons and Their Sides

5 sides: 6 sides: 7 sides:

9 sides:8 sides: 10 sides:

Pentagon Hexagon Heptagon

Octagon

Wed, Feb 02

Polygons and Their Sides

5 sides: 6 sides: 7 sides:

9 sides:8 sides: 10 sides:

Pentagon Hexagon Heptagon

Octagon

Wed, Feb 02

Polygons and Their Sides

5 sides: 6 sides: 7 sides:

9 sides:8 sides: 10 sides:

Pentagon Hexagon Heptagon

Octagon Nonagon

Wed, Feb 02

Polygons and Their Sides

5 sides: 6 sides: 7 sides:

9 sides:8 sides: 10 sides:

Pentagon Hexagon Heptagon

Octagon Nonagon

Wed, Feb 02

Polygons and Their Sides

5 sides: 6 sides: 7 sides:

9 sides:8 sides: 10 sides:

Pentagon Hexagon Heptagon

Octagon Nonagon Decagon

Wed, Feb 02

Polygons and Their Sides

5 sides: 6 sides: 7 sides:

9 sides:8 sides: 10 sides:

Pentagon Hexagon Heptagon

Octagon Nonagon Decagon

Wed, Feb 02

Polygons and Their Sides

5 sides: 6 sides: 7 sides:

9 sides:8 sides: 10 sides:

Pentagon Hexagon Heptagon

Octagon Nonagon Decagon

Anything larger:Wed, Feb 02

Polygons and Their Sides

5 sides: 6 sides: 7 sides:

9 sides:8 sides: 10 sides:

Pentagon Hexagon Heptagon

Octagon Nonagon Decagon

Anything larger: n-gon, where n is the number of sidesWed, Feb 02

Example 1

Name each polygon by its number of sides and label as concave or convex.

Wed, Feb 02

Example 1

Name each polygon by its number of sides and label as concave or convex.

Wed, Feb 02

Example 1

Name each polygon by its number of sides and label as concave or convex.

Concave

Wed, Feb 02

Example 1

Name each polygon by its number of sides and label as concave or convex.

ConcavePentagon

Wed, Feb 02

Example 1

Name each polygon by its number of sides and label as concave or convex.

ConcavePentagon

Convex

Wed, Feb 02

Example 1

Name each polygon by its number of sides and label as concave or convex.

ConcavePentagon

ConvexOctagon

Wed, Feb 02

Example 1

Name each polygon by its number of sides and label as concave or convex.

ConcavePentagon

ConvexOctagon

Convex

Wed, Feb 02

Example 1

Name each polygon by its number of sides and label as concave or convex.

ConcavePentagon

ConvexOctagon

ConvexQuadrilateral

Wed, Feb 02

Example 1

Name each polygon by its number of sides and label as concave or convex.

ConcavePentagon

ConvexOctagon

ConvexQuadrilateral

Concave

Wed, Feb 02

Example 1

Name each polygon by its number of sides and label as concave or convex.

ConcavePentagon

ConvexOctagon

ConvexQuadrilateral

ConcaveNonagon

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

# of sides:

# of triangles:

Degrees:

# of sides:

# of triangles:

Degrees:

# of sides:

# of triangles:

Degrees:

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3 # of sides:

# of triangles:

Degrees:

# of sides:

# of triangles:

Degrees:

# of sides:

# of triangles:

Degrees:

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

# of sides:

# of triangles:

Degrees:

# of sides:

# of triangles:

Degrees:

# of sides:

# of triangles:

Degrees:

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

180°

# of sides:

# of triangles:

Degrees:

# of sides:

# of triangles:

Degrees:

# of sides:

# of triangles:

Degrees:

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

180°

# of sides:

# of triangles:

Degrees:

4

# of sides:

# of triangles:

Degrees:

# of sides:

# of triangles:

Degrees:

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

180°

# of sides:

# of triangles:

Degrees:

4

# of sides:

# of triangles:

Degrees:

# of sides:

# of triangles:

Degrees:

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

180°

# of sides:

# of triangles:

Degrees:

4

2

# of sides:

# of triangles:

Degrees:

# of sides:

# of triangles:

Degrees:

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

180°

# of sides:

# of triangles:

Degrees:

4

2

360°

# of sides:

# of triangles:

Degrees:

# of sides:

# of triangles:

Degrees:

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

180°

# of sides:

# of triangles:

Degrees:

4

2

360°

# of sides:

# of triangles:

Degrees:

5 # of sides:

# of triangles:

Degrees:

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

180°

# of sides:

# of triangles:

Degrees:

4

2

360°

# of sides:

# of triangles:

Degrees:

5 # of sides:

# of triangles:

Degrees:

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

180°

# of sides:

# of triangles:

Degrees:

4

2

360°

# of sides:

# of triangles:

Degrees:

5 # of sides:

# of triangles:

Degrees:

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

180°

# of sides:

# of triangles:

Degrees:

4

2

360°

# of sides:

# of triangles:

Degrees:

5

3

# of sides:

# of triangles:

Degrees:

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

180°

# of sides:

# of triangles:

Degrees:

4

2

360°

# of sides:

# of triangles:

Degrees:

5

3

540°

# of sides:

# of triangles:

Degrees:

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

180°

# of sides:

# of triangles:

Degrees:

4

2

360°

# of sides:

# of triangles:

Degrees:

5

3

540°

# of sides:

# of triangles:

Degrees:

6

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

180°

# of sides:

# of triangles:

Degrees:

4

2

360°

# of sides:

# of triangles:

Degrees:

5

3

540°

# of sides:

# of triangles:

Degrees:

6

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

180°

# of sides:

# of triangles:

Degrees:

4

2

360°

# of sides:

# of triangles:

Degrees:

5

3

540°

# of sides:

# of triangles:

Degrees:

6

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

180°

# of sides:

# of triangles:

Degrees:

4

2

360°

# of sides:

# of triangles:

Degrees:

5

3

540°

# of sides:

# of triangles:

Degrees:

6

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

180°

# of sides:

# of triangles:

Degrees:

4

2

360°

# of sides:

# of triangles:

Degrees:

5

3

540°

# of sides:

# of triangles:

Degrees:

6

4

Wed, Feb 02

# of sides:

# of triangles:

Degrees:

3

1

180°

# of sides:

# of triangles:

Degrees:

4

2

360°

# of sides:

# of triangles:

Degrees:

5

3

540°

# of sides:

# of triangles:

Degrees:

6

4

720°

Wed, Feb 02

Angle Sum of a Polygon:

Angle Measure of a Regular Polygon:

Wed, Feb 02

Angle Sum of a Polygon: The sum of the interior angles of a polygon with n sides is given by the formula

Angle Measure of a Regular Polygon:

Wed, Feb 02

Angle Sum of a Polygon: The sum of the interior angles of a polygon with n sides is given by the formula

Angle Measure of a Regular Polygon: The measure of each interior angle of a regular polygon with n sides is given by the formula

S = (n − 2)180°n

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12S = (n − 2)180°

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12S = (n − 2)180°S = (6 − 2)180°

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

S = (4)180°

S = (n − 2)180°S = (6 − 2)180°

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

S = (4)180°

S = (n − 2)180°S = (6 − 2)180°

S = 720°

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

S = (4)180°

S = (n − 2)180°S = (6 − 2)180°

S = 720°The sum of all of the angles is 720°

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

2(10x) + 2(3x + 8) + 7x − 22 + 8x −12 = 720°

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

2(10x) + 2(3x + 8) + 7x − 22 + 8x −12 = 720°20x + 6x +16 + 7x − 22 + 8x −12 = 720°

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

2(10x) + 2(3x + 8) + 7x − 22 + 8x −12 = 720°20x + 6x +16 + 7x − 22 + 8x −12 = 720°

41x −18 = 720°

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

2(10x) + 2(3x + 8) + 7x − 22 + 8x −12 = 720°20x + 6x +16 + 7x − 22 + 8x −12 = 720°

41x −18 = 720°+18 +18

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

2(10x) + 2(3x + 8) + 7x − 22 + 8x −12 = 720°20x + 6x +16 + 7x − 22 + 8x −12 = 720°

41x −18 = 720°+18 +1841x = 738

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

2(10x) + 2(3x + 8) + 7x − 22 + 8x −12 = 720°20x + 6x +16 + 7x − 22 + 8x −12 = 720°

41x −18 = 720°+18 +1841x = 73841 41

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

2(10x) + 2(3x + 8) + 7x − 22 + 8x −12 = 720°20x + 6x +16 + 7x − 22 + 8x −12 = 720°

41x −18 = 720°+18 +1841x = 73841 41x = 18

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

x = 18

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

x = 18

10(18) =

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

x = 18

10(18) = 180°

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

x = 18

10(18) = 180° = m∠A = m∠B

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

x = 18

10(18) =

3(18) + 8 =

180° = m∠A = m∠B

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

x = 18

10(18) =

3(18) + 8 =

180°

62°

= m∠A = m∠B

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

x = 18

10(18) =

3(18) + 8 =

180°

62°

= m∠A = m∠B

= m∠C = m∠D

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

x = 18

10(18) =

3(18) + 8 =

180°

62°

7(18) - 22 =

= m∠A = m∠B

= m∠C = m∠D

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

x = 18

10(18) =

3(18) + 8 =

180°

62°

7(18) - 22 = 104°

= m∠A = m∠B

= m∠C = m∠D

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

x = 18

10(18) =

3(18) + 8 =

180°

62°

7(18) - 22 = 104°

= m∠A = m∠B

= m∠C = m∠D

= m∠E

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

x = 18

10(18) =

3(18) + 8 =

180°

62°

7(18) - 22 = 104°

8(18) - 12 =

= m∠A = m∠B

= m∠C = m∠D

= m∠E

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

x = 18

10(18) =

3(18) + 8 =

180°

62°

7(18) - 22 = 104°

8(18) - 12 = 132°

= m∠A = m∠B

= m∠C = m∠D

= m∠E

Wed, Feb 02

Example 2

In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of

the angles of the hexagon, then find the measure of each angle.A

B

C

D

E

F

10x

10x

3x + 8

3x + 8

7x - 22

8x - 12

x = 18

10(18) =

3(18) + 8 =

180°

62°

7(18) - 22 = 104°

8(18) - 12 = 132°

= m∠A = m∠B

= m∠C = m∠D

= m∠E

= m∠F

Wed, Feb 02

Example 3

Find the measure of each angle of a regular 14-gon.

Wed, Feb 02

Example 3

Find the measure of each angle of a regular 14-gon.

S = (n − 2)180°n

Wed, Feb 02

Example 3

Find the measure of each angle of a regular 14-gon.

S = (n − 2)180°n

S = (14 − 2)180°14

Wed, Feb 02

Example 3

Find the measure of each angle of a regular 14-gon.

S = (n − 2)180°n

S = (14 − 2)180°14

S = (12)180°14

Wed, Feb 02

Example 3

Find the measure of each angle of a regular 14-gon.

S = (n − 2)180°n

S = (14 − 2)180°14

S = (12)180°14

S = 2160°14

Wed, Feb 02

Example 3

Find the measure of each angle of a regular 14-gon.

S = (n − 2)180°n

S = (14 − 2)180°14

S = (12)180°14

S = 2160°14

S = 154 2 7°

Wed, Feb 02

Problem Set

Wed, Feb 02

Problem Set

p. 224 #1-33 odd

“Liberty without learning is always in peril; learning without liberty is always in vain.” - John F. Kennedy

Wed, Feb 02