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Angle Measures in Regular Polygons: Example Solutions

Learn how to find angle measures in regular pentagons and squares using central angles. Explore solutions step by step.

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Angle Measures in Regular Polygons: Example Solutions

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  1. In the diagram, ABCDEis a regular pentagon inscribed in F. Find each angle measure. 360° 5 a. m AFB AFB is a central angle,som AFB = , or 72°. 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 andm AFG = m AFB = 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. ANSWER P, PY or XP, PQ, XPY. for Example 1 GUIDED PRACTICE

  5. 2. Find m XPY, m XPQ, andm PXQ. ANSWER 90°, 45°, 45° for Example 1 GUIDED PRACTICE

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