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EXAMPLE 1

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

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EXAMPLE 1

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

  2. In the diagram, ABCDEis a regular pentagon inscribed in F. Find each angle measure. b. m AFG FG is an apothem, which makes it an altitude ofisosceles ∆AFB. So, FGbisectsAFB andmAFG = mAFB = 36°. 1 2 Find angle measures in a regular polygon EXAMPLE 1 SOLUTION

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

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

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

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

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

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