aim: how do we find angle measures in polygons? a polygon is a closed figure whose sides are line...
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Aim: How do we find angle measures in polygons?
A polygon is a closed figure whose sides are line segments that intersect only at their endpoints.
In a regular polygon , all the angles have the same measures and all the sides have the same length.
Polygons can be indentified by the number of their sides
Regular PolygonsPolygons
Not Polygons
Aim: How do we find angle measures in polygons?
Practice- Is the shape a polygon, a regular polygon or not a polygon?
1.
Not a Polygon –The sides are not line segments.
2. 3.
Regular Polygon – All the sides and angles have the same measure.
Polygon – All the sides are line segments.
Aim: How do we find angle measures in polygons?
Aim: How do we find angle measures in polygons?A vertex is a point where two sides meet.
The interior angles of a polygon are the angles inside the polygon.
A diagonal of a polygon is a line segment that joins two nonconsecutive vertices.
What is the sum of the measures of the interior angles of a quadrilateral?
Vertex
Interior Angles
Diagonal
Since the quadrilateral is made up of 2 triangles, the sum the angles is 2(180o) = 360o
Aim: How do we find angle measures in polygons?You can use triangles to find these sum of the angle measures in other figures.
Shape Quadrilateral Pentagon Hexagon Heptagon
Number of Sides
Number of Diagonals from one vertex
Number of Triangles Formed
Sum of Angle Measures
Sum of angle measures in an n-gon = (n-2) 180Sum of angle measures in an n-gon = (n-2) 180
4
1
2
2(180o)=360o
5
2
3
3(180o)=540o
6
3
4
4(180o)=720o
7
4
5
5(180o)=900o
13-gon n-gon
13
10
11
11(180o)=1980o
n
n-2
(n-2)180o
Aim: How do we find angle measures in polygons?
1. Find the sum of the measures of the interior angles of octagon.
An octagon has 8 sides, so n=8.
(n-2)180
(8-2)180
(6)180
1,080 o
2. Find the sum of the measures of the interior angles of an 11-gon.
A 11-gon has 11 sides, so n=11.
(n-2)180
(11-2)180
(9)180
1,620 o
Sum of an angle measures in an n-gon = (n-2) 180Sum of an angle measures in an n-gon = (n-2) 180
Aim: How do we find angle measures in polygons?Find the sum of the measures of the interior angles in the polygon.
3) 14-gon 4) 17-gon 5) 19-gon
Aim: How do we find angle measures in polygons?Remember, in a regular polygon, all the angles have the same measure.
HexagonRegularHexagon
6) Find the measure of one angle in a regular hexagon.
(n-2)180
(6-2)180
(4)180
720 o
720 ÷ 6 = 120 o
120 o
120 o120 o
120 o
120 o 120 o
Aim: How do we find angle measures in polygons?
Measure of one angle in a regular n-gon = (n-2) 180. nMeasure of one angle in a regular n-gon = (n-2) 180. n
Sum of an angle measures in an n-gon = (n-2) 180Sum of an angle measures in an n-gon = (n-2) 180
7) Find the measure of one angle in a regular octagon.
A regular octagon has 8 sides, so n=8.
= (n-2)180 n
= (8-2)180 8
= (6)180 8
= 1080 8
= 135 o
One angle in a regular octagon is 135 o.
8) Find the measure of one angle in a regular 14-gon. Round to the nearest tenth of a degree.A regular 14-gon has 14 sides, so n=14.
= (n-2)180 n
= (14-2)180 14
= (12)180 14
= 2160 14
= 154.3 o
One angle in a regular 14-gon is 154.3 o.
Aim: How do we find angle measures in polygons?Find the measure of one angle in the polygon.
9) Regular 12-gon 10) Regular 16-gon 11) Regular 20-gon
Aim: How do we find angle measures in polygons?Indentify the Polygon
12) The sum of the measures of the interior angles in a polygon is 1,440 o. What type of polygon is it?
1440 = (n-2)180
1800 = 180n
180 180
1440 = 180n-360
10 = n
Sum of an angle measures in an n-gon = (n-2) 180Sum of an angle measures in an n-gon = (n-2) 180
A polygon interior angles that has a sum of 1440o is a decagon.
Aim: How do we find angle measures in polygons?Practice- Identify the polygon whose interior angles have the following sum.
13) 1800o 14) 1260o 15) 3420o
Aim: How do we find angle measures in polygons?Find the value of x.
16) 115o
xo 98o
xo140o
175o
150o
(n-2)180
(6-2)180
(4)180
=720 o
720 = 98+140+175+150+x
720 = 563 +x
157 = x
17)
Aim: How do we find angle measures in polygons?Find the value of x.
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Aim: How do we find angle measures in polygons?
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Aim: How do we find angle measures in polygons?
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Aim: How do we find angle measures in polygons?
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