Measures of Angles of Measures of Angles of PolygonsPolygons

B.2.1.1 Determine the total number of degrees in the interior angles of a polygon in 3-8 sided figures (formula provided on the reference sheet).

B.2.1.2 Determine the measurement of one interior angle of a regular polygon (3-8 sided polygons, formula provided on the reference sheet).

B.2.1.3 Determine the number of degrees in the interior angles (3 - 8 sided polygons, formula provided on the reference sheet).

PA Standards

Definition:

A polygon is a closed figure with line segments for sides. Polygons can have any number of sides.

** The sum of the measures of the angles in any triangle is 1800.

Use the following formula to find the sum of the measures of the angles of a polygon.

180 x (n - 2)

n = the number of sides in the polygon

** this formula is on the reference sheet

Find the sum of the measure of the angles of the pentagon.

Find the sum of the measure of all angles in this polygon.

Quintana measures the angles of a polygon Quintana measures the angles of a polygon and finds that the sum is 360and finds that the sum is 36000. What kind of . What kind of polygon did she measure?polygon did she measure?

A regular polygon is a special type of a figure that has congruent sides and congruent

angles.

To find the measure of any interior angle in a regular polygon, you can use the formula

180 (n - 2) n

n = the number of sides in the polygonn = the number of sides in the polygon

What is the measure of one interior angle in What is the measure of one interior angle in a regular hexagon?a regular hexagon?

How many degrees are there in a 7-sided How many degrees are there in a 7-sided polygon?polygon?

What is the measure of Z?

Z

X

Y

450

150

300

1200

1800

900

What is the measure of one of the angels in an equilateral triangle?

300

600

900

1200

How many sides does a polygon with a total angle measure of 5400 have?

3

4

5

6

How many degrees does a hexagon have?

3600

7200

9000

10800

What is the sum of the measures of the angles in this polygon?

1800

3600

5400

7200

How many sides does a polygon with 9000 have?

5

6

7

8

The four angles of quadrilateral ABCD have the same measure. What is the measure of each angle?

450

600

900

1200

What is the measure of F?

A

B

CD

E

F

1320

950

1240

1340

1030

900

1000

1100

1200

Which figure or combination of figures has the greatest total measure of angels?

hexagon and one triangle

three triangles

two quadrilaterals

octagon

What is the measure opf each interior angle of a regular octagon?

1080

1350

1600

1720