Download Unit 5 - Lesson 5.2 - Angles of a Polygon

Geometry
Unit 5: Lesson 5.2
Name: _______________________________
Date: _________________ Period: _______
Angles of Polygons (Textbook Section 6.2)
Essential Questions:
o
What is the relationship between the number of sides and the measure of each interior/exterior angle
of a regular convex polygon?
Goal:
 I can understand how to find measures of angles of polygons.
Theorems:
Finding the diagonals
of a polygon
Section 1: Sum of Polygon Angle Measures
1) Find the sum of the interior angle measures of
a convex octagon.
YT 1) Find the sum of the interior angle measures
of a convex nonagon.
Answer:
2) Find the sum of the interior angles of a regular
20-gon.
Answer:
YT 2) Find the sum of the interior angle measures
of a convex 15-gon.
Answer:
Answer:
Section 2: The Interior Angles of a Regular Polygon and Polygon
3) Find the measure of each interior angle of a
YT 3) Find the measure of each interior angle of a
regular decagon.
regular nonagon.
Answer:
4) Find the measure of each interior angle of
quadrilateral PQRS.
Answer:
YT 4) Find the measure of each interior angle of a
regular dodecagon.
Answer:
5) Find the value of x.
Answer:
YT 5) Find the value of x.
Answer:
Answer:
Section 3: Finding Exterior Angle Measures in Polygons
6) Find the measure of each exterior angle of a
YT 6) Find the measure of each exterior angle of a
regular hexagon.
regular dodecagon.
Answer:
7) Find the value of a in polygon RSTUV.
Answer:
YT 7) Find the value of r in polygon MJKL.
Answer:
Answer:
8) Find the value of x.
YT 8) Find the value of x.
Answer:
Answer:
Section 4: Finding the Number of Sides of a Polygon
9) The measure of each interior angle of a regular YT 9) The measure of each interior angle of a
polygon is 140  . How many sides does the
regular polygon is 157.5 . How many sides does
polygon have?
the polygon have?
Answer:
10) The measure of each exterior angle of a
regular polygon is 72  . How many sides does the
polygon have?
Answer:
YT 10) The measure of each exterior angle of a

regular polygon is 24 . How many sides does the
polygon have?
Answer:
Section 5: Diagonals of a Polygon
11) How many diagonals does an octagon have?
Answer:
Answer:
12) How many diagonals does an 18-sided
polygon have?
Answer:
YT 12) How many diagonals does an 33-sided
polygon have?
YT 11) How many diagonals does a triangle have?
Answer:
Answer:
Section 6: Extension
13) Polygon PQRST is a regular pentagon. Find the values of x, y, and z.
Answer:
Homework:
Textbook: Pg. 276 – 277 # 1 – 32
Lesson Summary:
Draw a regular convex polygon and a convex polygon that is not regular
with the same number of sides. Find the sum interior angles for each.