Download Polygons - Mrs Might PreAP Geometry

Name ___________________________________
Period _____________
Date ____________
8.1 Angles in a Polygon
Pre-AP Geometry
EXPLORE/EXPLAIN
1) Sum of the interior angles
Triangle Angle-Sum Theorem states that the sum of the interior angles of a triangle is 180°. Now you can use
this theorem to investigate the sum of the measures of the interior angles of any polygon.
Work with a partner. Record your data in the table below.
a. Sketch polygons with 4, 5, 6, 7, and 8 below.
b. Divide each polygon into triangles by drawing all the diagonals from one vertex.
c. Multiply the number of triangles by 180° to find the sum of the measures of the interior
angles of each polygon.
d. Write a conjecture for finding the sum of the measures of the interiors angles of a polygon
with “n” sides.
Name of polygon
Sketch of polygon Number of sides
Number of
Sum of the
triangles formed
interior angle
measures
Quadrilateral
4
Pentagon
n-gon
n
2) Find the sum of the measures of the interior angles for each polygon.
____________ 1) 15-gon
____________ 2) 20-gon
____________ 3) decagon
____________ 4) dodecagon
3) Sum of the exterior angles
The figures below show one exterior angle drawn at each vertex of each polygon. Work with your
partner and record your data in the table below.
a. Calculate the sum of the measures of the exterior angles of each polygon.
b. Make a conjecture about the sum of the measures of the exterior angles of a polygon with
“n” sides.
Column 1
Polygons
4
Sum of the measures of
the interior angles
Column 2
Exterior Angle Sum
number of
linear pairs x 180
Sum of the exterior angle
measures (column 2 column 1)
3(180)=540
540-180= _______
(m1+m2+m3) =
1
2
3
5
6
8
4
5 1
2
6
180
(m1+m2+m3+m4)
3 7
10
6 1
5
4 9
2
3
7
8
2
n-gon
4. What is the formula to find the sum of the interior angles of a convex polygon with n sides?
Sum of Interior s of convex polygon =
5. What is the formula to find ONE interior angle of a regular polygon with n sides?
One Interior  of regular polygon =
6. What is the formula for the sum of the exterior angles of a convex polygon with n sides?
Sum of Exterior s of convex polygon =
7. What is the formula to find ONE exterior angle of a regular polygon with n sides?
One Exterior  of regular polygon =