University:
College Entrance Preparation
Course:
ACT Preparation (Mathematics)
Academic year:

2024
Views:

17

Pages:

4
Author:

imophulebf7

Geometry: 7.1-7.3 Notes NAME: Date: 7.1 Angles of Polygons Define Vocabulary: diagonal - a segment that joins two nonconsecutive vertices of a polygon equilateral polygon - a polygon in which all sides are congruent equiangular polygon - a polygon in which all angles are congruent regular polygon - a convex polygon that is both equilateral and equiangular Using Interior Angles Measures of Polygons In a polygon, two vertices that are endpoints of the same side are called consecutive vertices. A diagonal of a polygon is a segment that joins two nonconsecutive vertices. [Image of a polygon ABCDE with diagonals labeled] A and B are consecutive vertices. Vertex B has two diagonals, BD and BE. Theorems Theorem 7.1 Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex n-gon is (n-2)180°. m∠1 + m∠2 + ... + m∠n = (n-2)180° [Image of a polygon with n sides and angles labeled 1 through n] Examples: Finding an unknown exterior angle measure. 9. WE DO Find the value of x in the diagram. [Image of a polygon with angles labeled] 5x + 62 + 35 + 69 + 41 + 58 = 360 5x + 265 = 360 5x = 95 x = 19 10. YOU DO A convex hexagon has exterior angles with measures 34°, 49°, 58°, 67°, and 75°. What is the measure of an exterior angle at the 6th vertex? x + 34 + 49 + 58 + 67 + 75 = 360 x + 283 = 360 -283 -283 x = 77° Examples: Finding angle measure of regular polygons. 11. WE DO Each face of the dodecahedron is shaped like a regular pentagon. a. Find the measure of each interior angle of a regular pentagon. (5-2)180 = 540/5 = 108° b. Find the measure of each exterior angle of a regular pentagon. 360/5 = 72° 12. YOU DO a. Find the measure of each interior angle and each exterior angle of a regular 24-gon. (24-2)180 = 3960/24 = 165° 360/24 = 15° b. Each exterior angle of a regular polygon has a measure of 18°. Find the number of sides of the regular polygon. 360/n = 18 18n = 360 n = 20