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Transcript
7-8 Angles in Polygons Learn to find the measures of angles in polygons. Course 2 7-8 Angles Insert Lesson Title Here in Polygons Vocabulary diagonal Course 2 7-8 Angles in Polygons Additional Example 1: Determining the Measure of an Unknown Interior Angle Find the measure of the unknown angle. 55° 80° x 80° + 55° + x = 180° The sum of the measures of the angles is 180°. 135° + x = 180° Combine like terms. –135° –135° Subtract 135° from both sides. x= 45° The measure of the unknown angle is 45°. Course 2 7-8 Angles in Polygons Try This: Example 1 Find the measure of the unknown angle. 30° 90° x 90° + 30° + x = 180° The sum of the measures of the angles is 180°. 120° + x = 180° Combine like terms. –120° –120° Subtract 120° from both sides. x= 60° The measure of the unknown angle is 60°. Course 2 7-8 Angles in Polygons The sum of the angle measures in other polygons can be found by dividing the polygon into triangles. A polygon can be divided into triangles by drawing all of the diagonals from one of its vertices. Course 2 7-8 Angles in Polygons A diagonal of a polygon is a segment that is drawn from one vertex to another and is not one of the sides of the polygon. You can divide a polygon into triangles by using diagonals only if all of the diagonals of that polygon are inside the polygon. The sum of the angle measures in the polygon is then found by combining the sums of the angle measures in the triangles. Course 2 7-8 Angles in Polygons Number of triangles in pentagon 3 Course 2 Sum of angle measures in each triangle · 180° Sum of angle measures in pentagon = 540° 7-8 Angles in Polygons Additional Example 2A: Drawing Triangles to Find the Sum of Interior Angles Divide each polygon into triangles to find the sum of its angle measures. A. 6 · 180° = 1080° There are 6 triangles. The sum of the angle measures of an octagon is 1,080°. Course 2 7-8 Angles in Polygons Additional Example 2B: Drawing Triangles to Find the Sum of Interior Angles Divide each polygon into triangles to find the sum of its angle measures. B. 10 · 180° = 1,800° There are 10 triangles. The sum of the angle measures of a 12-sided polygon is 1,800°. Course 2 7-8 Angles in Polygons Try This: Example 2A Divide each polygon into triangles to find the sum of its angle measures. A. 4 · 180° = 720° There are 4 triangles. The sum of the angle measures of a hexagon is 720°. Course 2 7-8 Angles in Polygons Try This: Example 2B Divide each polygon into triangles to find the sum of its angle measures. B. 2 · 180° = 360° There are 2 triangles. The sum of the angle measures of a square is 360°. Course 2 7-8 Angles in Polygons Formula for Sum of Interior Angles The sum of interior angles is equal to the number of sum = 180(n – 2)o o sides minus 2 times 180 . where n is the number of sides Course 2 7-8 Angles in Polygons Formula for Sum of Interior Angles Use the formula to find the sum of its angle measures. A. sum = 180(8 – 2)° sum = 180(6)° There are 8 sides. The sum of the angle measures of an octagon is 1,080°. Course 2 7-8 Angles in Polygons Formula for Sum of Interior Angles Use the formula to find the sum of its angle measures. B. sum = 180(10 – 2)° There are 10 sides. sum = 180(8)° The sum of the angle measures of an decagon is 1,440°. Course 2 7-8 Angles Insert Lesson in Polygons 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 obtuse triangle with angle measures of 42° and 32° 106° 4. Divide a seven-sided polygon into triangles to find the sum of its interior angles *Or use the formula* 900° Course 2 Homework 7-8 Worksheet Study for fraction quiz Thursday Study for 7-2 to 7-8 quiz Thursday