6.1. Angles in Polygons http://www.ck12.org
24.
25.
26.
- The interior angles of a pentagon arex◦,x◦, 2 x◦, 2 x◦, and 2x◦. What is the measure of the larger angles?
- The exterior angles of a quadrilateral arex◦, 2 x◦, 3 x◦, and 4x◦. What is the measure of the smallest angle?
- The interior angles of a hexagon arex◦,(x+ 1 )◦,(x+ 2 )◦,(x+ 3 )◦,(x+ 4 )◦, and(x+ 5 )◦. What isx?
30.ChallengeEach interior angle forms a linear pair with an exterior angle. In a regular polygon you can use two
different formulas to find the measure of each exterior angle. One way is^360
◦
n and the other is 180
◦−(n−^2 )^180 ◦
n
(180◦minus Equiangular Polygon Formula). Use algebra to show these two expressions are equivalent.
31.Angle PuzzleFind the measures of the lettered angles below given thatm||n.Review Queue Answers
a. 72◦+( 7 x+ 3 )◦+( 3 x+ 5 )◦= 180 ◦
10 x+ 80 ◦= 180 ◦
10 x= 100 ◦
x= 10 ◦
b.( 5 x+ 17 )◦+( 3 x− 5 )◦= 180 ◦
8 x+ 12 ◦= 180 ◦