Tips For Success

Some test questions ask you to find the measure of an interior or exterior angle of a polygon. Read the sample question below. Then follow the tips to answer it.

In the figure below, ABCDE is a regular pentagon. What is the measure, in degrees, of ∠ A B E ? angle eh b e question mark

1. 36
2. 54
3. 72
4. 108

Think It Through

By the Polygon Angle-Sum Theorem, the sum of the interior angle measures of ABCDE is ( 5 − 2 ) 180 = 3 ( 180 ) = 540 . open 5 minus . 2 close 180 equals 3 . open 180 close , equals 540 , .  So m ∠ A = 540 5 = 108 . m angle eh equals , 540 over 5 , equals 108 .  Then 108 + m ∠ A B E + m ∠ A E B = 180 . 108 plus , m angle eh b e plus m angle eh e b , equals 180 , .  Since ∠ A B E ≅ ∠ A B E , 108 + 2 · m ∠ A B E = 180 . angle eh b e approximately equal to angle eh b e comma , 108 plus . 2 middle dot , m angle eh b e , equals 180 , .  So m ∠ A B E = 180 − 108 2 = 72 2 = 36 . m angle eh b e equals . fraction 180 minus 108 , over 2 end fraction . equals , 72 over 2 , equals 36 .

The correct answer is A.