1. EXAMPLE 1 Find angle measures in a regular polygon a. m AFB In the diagram, ABCDE is a regular pentagon inscribed in F. Find each angle measure. SOLUTION AFB is a central angle, so m AFB =, or 72 °. 360 ° 5

2. EXAMPLE 1 Find angle measures in a regular polygon b. m AFG In the diagram, ABCDE is a regular pentagon inscribed in F. Find each angle measure. SOLUTION FG is an apothem, which makes it an altitude of isosceles ∆AFB. So, FG bisects AFB and m AFG = m AFB = 36 °. 1 2

3. EXAMPLE 1 Find angle measures in a regular polygon c. m GAF In the diagram, ABCDE is a regular pentagon inscribed in F. Find each angle measure. SOLUTION The sum of the measures of right ∆GAF is 180 °. So, 90 ° + 36 ° + m GAF = 180 °, and m GAF = 54 °.

4. GUIDED PRACTICE for Example 1 In the diagram, WXYZ is a square inscribed in P. 1. Identify the center, a radius, an apothem, and a central angle of the polygon.

5. GUIDED PRACTICE for Example 1 SOLUTION center – P radius – PY or XP an apothem – PQ central angle – XPY

6. GUIDED PRACTICE for Example 1 2. Find m XPY, m XPQ, and m PXQ. m XPY is a central angle so m XPY = 4 360 = XPQ = 45 ° SOLUTION m XPY = 90 ° QP is an apothem, which make it an altitude of isosceles ∆ XPQ so QP bisects XPY and m XPQ = m 1 2

7. GUIDED PRACTICE for Example 1 90 ° + 45 + m PXQ = 180 and PXQ = 45 ° The sum of measures of right ∆ PXQ is 180° so