AMSCO'S Geometry. New York - Rye High School

370 Parallel LinesEXAMPLE 1The measure of an exterior angle of a regular polygon is 45 degrees.a. Find the number of sides of the polygon.b. Find the measure of each interior angle.c. Find the sum of the measures of the interior angles.Solutiona. Let n be the number of sides of the polygon. Then the sum of the measuresof the exterior angles is n times the measure of one exterior angle.45n 5 360n 5 36045n 5 8 Answerb. Each interior angle is the supplement of each exterior angle.Measure of each interior angle 180 45 135 Answerc. Use the sum of the measures of the interior angles, 180(n 2).180(n 2 2) 5 180(8 2 2)5 180(6)5 1,080orAnswerMultiply the measure of each interior angle by the number of sides.8(135) 1,080 AnswerAnswers a. 8 sides b. 135° c. 1,080°EXAMPLE 2In quadrilateral ABCD, mA x, mB 2x 12, mC = x 22, andmD 3x.a. Find the measure of each interior angle of the quadrilateral.b. Find the measure of each exterior angle of the quadrilateral.Solution a. mA mB mC mD 18(n 2)x 2x 12 x 22 3x 180(4 2)7x 10 3607x 350x 50