1. 8-8 Angles in Polygons Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Warm Up Solve. 1. 72 + 18 + x = 180 2. 80 + 70 + x = 180 3. x + 42 + 90 = 180 4. 120 + x + 32 = 180 x = 90 x = 30 x = 48 Course 2 8-8 Angles in Polygons x = 28

3. Problem of the Day How many different rectangles are in the figure shown? 100 Course 2 8-8 Angles in Polygons

4. Learn to find the measures of angles in polygons. Course 2 8-8 Angles in Polygons

5. Course 2 8-8 Angles in Polygons If you tear off the corners of a triangle and put them together, you will find that they form a straight angle. This suggests that the sum of the measures of the angles in a triangle is 180°.

6. Course 2 8-8 Angles in Polygons Angles of a Triangle The sum of the measures of the angles in a triangle is 180 °. m  1 + m  2 + m  3 = 180 ° 1 3 2

7. Find the measure of the unknown angle. Additional Example 1: Finding an Angle Measure of in a Triangle Course 2 8-8 Angles in Polygons 55° 80° x 80° + 55° + x = 180° 135° + x = 180° –135° x = 45° The measure of the unknown angle is 45°. The sum of the measures of the angles is 180°. Combine like terms. Subtract 135° from both sides.

8. Course 2 8-8 Angles in Polygons Angles of a Quadrilateral The sum of the measures of the angles in a quadrilateral is 360 °. m  1 + m  2 + m  3 + m  4 = 360 ° 1 2 4 3

9. Find the unknown angle measure in the quadrilateral. Additional Example 2: Finding an Angle Measure of in a Quadrilateral Course 2 8-8 Angles in Polygons 65° + 89° + 82° + x = 360° 236° + x = 360° –236° x = 124° The measure of the unknown angle is 124°. The sum of the measures of the angles is 360°. Combine like terms. Subtract 236° from both sides. 65° x 89° 82°

10. Divide each polygon into triangles to find the sum of its angle measures. Additional Example 3: Drawing Triangles to Find the Sum of Interior Angles Course 2 8-8 Angles in Polygons There are 6 triangles. The sum of the angle measures of an octagon is 1,080°. 6 · 180° = 1080°

11. Divide each polygon into triangles to find the sum of its angle measures. Check It Out: Example 3 Course 2 8-8 Angles in Polygons There are 4 triangles. The sum of the angle measures of a hexagon is 720°. 4 · 180° = 720°

12. Lesson Quiz 54° 37° Insert Lesson Title Here 84° 720° Course 2 8-8 Angles in Polygons Find the measure of the unknown angle for each of the following. 1. a triangle with angle measures of 66° and 77° 2. a right triangle with one angle measure of 36° 3. an quadrilateral with angle measures of 144°, 84°, and 48°. 4. Divide a six-sided polygon into triangles to find the sum of its interior angles