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Find and use the measures of interior and exterior angles of polygons.

6.1: Polygon Angle Theorems. Objectives. Find and use the measures of interior and exterior angles of polygons. Handbook p. 19. Polygon Angle Sum Theorem: The sum of the interior angles of a convex polygon is ( n  2) 180. Draw each diagonal from a single vertex, then complete the chart.

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Find and use the measures of interior and exterior angles of polygons.

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  1. 6.1: Polygon Angle Theorems Objectives Find and use the measures of interior and exterior angles of polygons. Handbook p. 19

  2. Polygon Angle Sum Theorem: The sum of the interior angles of a convex polygon is (n 2) 180. Draw each diagonal from a single vertex, then complete the chart.

  3. 6.1: Polygon Angle Theorems 1. Find the sum of the interior angle measures of a convex heptagon. (n – 2)180° (7 – 2)180° 900°

  4. 6.1: Polygon Angle Theorems 2. Find the measure of each interior angle of a regular 16-gon. Step 1:Find the sum of the interior angle measures. (n – 2)180° (16 – 2)180° = 2520° Step 2:Find the measure of one interior angle.

  5. Handbook page 19

  6. 6.1: Polygon Angle Theorems 3. Find the measure of each interior angle of pentagon ABCDE. (5 – 2)180° = 540° 35c + 18c+ 32c+ 32c+ 18c= 540 135c= 540 c= 4 mA= 35(4°)= 140° mB = mE = 18(4°)= 72° mC = mD = 32(4°)= 128°

  7. 6.1: Polygon Angle Theorems 4a. What is the measure of each interiorangle of a regular decagon? b. What is the measure of eachexteriorangle of a regular decagon? c. What is the SUM of allof the exterior angles?

  8. 6.1: Polygon Angle Theorems In the polygons below, an exterior angle has been measured at each vertex. Notice that in each case, the sum of the exterior angle measures is 360°.

  9. Measure of one ext.  = 5. Find the measure of each exterior angle of a regular 20-gon. A 20-gon has 20 sides and 20 vertices. Sum of ext. s = 360°. The measure of each exterior angle of a regular 20-gon is 18°.

  10. Angle measures of a convex polygon with n sides

  11. 6. Find the value of b in polygon FGHJKL. 15b° + 18b° + 33b° + 16b° + 10b° + 28b°= 360° 120b= 360 b= 3

  12. 7. Name the convex polygon whose sum of its interior angle measures is 6840. 8. The exterior angle of a regular polygon is about 27.7. Find the number of its sides and the measure of each interior angle.

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