Lesson Vocabulary

• radius of a regular polygon
• apothem

Problem 1 Finding Angle Measures

The figure below is a regular pentagon with radii and an apothem drawn. What is the measure of each numbered angle?

m ∠ 1 = 360 5 = 72 Divide  360   by the number of sides. m ∠ 2 = 1 2 m ∠ 1 The apothem bisects the vertex angle of the isosceles triangle formed by the radii.   = 1 2 ( 72 ) = 36   table with 3 rows and 3 columns , row1 column 1 , m angle 1 , column 2 equals , 360 over 5 , equals 72 , column 3 cap divide . 360 . by the number of sides. , row2 column 1 , m angle 2 , column 2 equals , 1 half , m angle 1 , column 3 table with 2 rows and 1 column , row1 column 1 , cap the apothem bisects the vertex angle of the , row2 column 1 , isosceles triangle formed by the radii. , end table , row3 column 1 , , column 2 equals , 1 half , open 72 close equals 36 , column 3 , end table

90 + 36 + m ∠ 3 = 180 The sum of the measures of the angles of a triangle is  180. m ∠ 3 = 54   m ∠ 1 = 72 , m ∠ 2 = 36 ,  and m ∠ 3 = 54. table with 3 rows and 3 columns , row1 column 1 , 90 plus 36 plus m angle 3 , column 2 equals 180 , column 3 cap thesumofthemeasuresoftheanglesofatriangleis . 180. , row2 column 1 , m angle 3 , column 2 equals 54 , column 3 , row3 column 1 , m angle 1 equals 72 comma m angle 2 , column 2 equals 36 comma , and , column 3 m angle 3 equals 54. , end table

✓ Got It?

1. Below, a portion of a regular octagon has radii and an apothem drawn. What is the measure of each numbered angle?