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

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Find Angle Measure in Polygons

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

Warm Up Solve x = x = x = x + 32 = 180 x = 90 x = 30 x = 48 Course Angles in Polygons x = 28

Problem of the Day How many different rectangles are in the figure shown? 100 Course Angles in Polygons

Learn to find the measures of angles in polygons. Course Angles in Polygons

Course 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°.

Course 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

Find the measure of the unknown angle. Additional Example 1: Finding an Angle Measure of in a Triangle Course 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.

Course 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 °

Find the unknown angle measure in the quadrilateral. Additional Example 2: Finding an Angle Measure of in a Quadrilateral Course 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°

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 Angles in Polygons There are 6 triangles. The sum of the angle measures of an octagon is 1,080°. 6 · 180° = 1080°

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

Lesson Quiz 54° 37° Insert Lesson Title Here 84° 720° Course 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