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**8-8**Angles in Polygons Course 2 Warm Up Problem of the Day Lesson Presentation**8-8**Angles in Polygons Course 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 x = 28**8-8**Angles in Polygons Course 2 Problem of the Day How many different rectangles are in the figure shown? 100**8-8**Angles in Polygons Course 2 Learn to find the measures of angles in polygons.**8-8**Angles in Polygons Course 2 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°.**8-8**Angles in Polygons Course 2 2 3 1**8-8**Angles in Polygons Course 2 Additional Example 1: Finding an Angle Measure of in a Triangle 55° Find the measure of the unknown angle. 80° x The sum of the measures of the angles is 180°. 80° + 55° + x = 180° 135° + x = 180° Combine like terms. –135° –135° Subtract 135° from both sides. x = 45° The measure of the unknown angle is 45°.**8-8**Angles in Polygons 2 3 1 4 Course 2**8-8**Angles in Polygons 89° 82° 65° x Course 2 Additional Example 2: Finding an Angle Measure of in a Quadrilateral Find the unknown angle measure in the quadrilateral. The sum of the measures of the angles is 360°. 65° + 89° + 82° + x = 360° 236° + x = 360° Combine like terms. –236° –236° Subtract 236° from both sides. x = 124° The measure of the unknown angle is 124°.**8-8**Angles in Polygons Course 2 Additional Example 3: Drawing Triangles to Find the Sum of Interior Angles Divide each polygon into triangles to find the sum of its angle measures. 6 · 180° = 1080° There are 6 triangles. The sum of the angle measures of an octagon is 1,080°.**8-8**Angles in Polygons Course 2 Check It Out: Example 3 Divide each polygon into triangles to find the sum of its angle measures. 4 · 180° = 720° There are 4 triangles. The sum of the angle measures of a hexagon is 720°.**8-8**Angles in Polygons Course 2 Insert Lesson Title Here Lesson Quiz Find the measure of the unknown angle for each of the following. 1. a triangle with angle measures of 66° and 77° 37° 2. a right triangle with one angle measure of 36° 54° 3. an quadrilateral with angle measures of 144°, 84°, and 48°. 84° 4. Divide a six-sided polygon into triangles to find the sum of its interior angles 720°