# Easy geometry questions involving interior and exterior angles..help?

1) Each interior angle of a regular polygon has a measure of 90, find the total number of sides of the polygon. (I know the answer is 4 sides, I just don't know how to show work)

2) In parallelogram RSTW, the measure of an exterior angle at R is 115. What is the measure of angle T?

(completely lost on this one.)

Relevance

1) int + ext =180

90 + ext =180

ext= 90

ext = 360/n where n is the number of sides

n =360/90

n = 4

2) ext R =115

line RS is a straight, and if extend line TS, then RW & ST r parallel

by alternate angles, ang.RST=115

BY CO-INTERIOR angles

180-115=65

ang.T or STW =65.

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• In a 30-60-ninety triangle, the leg between 60 and ninety is x in length (that's the shortest leg), the leg between 30 and ninety is x*sqrt(3) (that's the longest leg), and the hypotenuse (between 30 and 60) is 2x. you realize that the shorter leg is two, so x = 2. Now evaluate for the different lengths: Longer leg: x*sqrt(3) 2sqrt(3) or approximately 3.40 six <===answer Hypotenuse: 2x 2(2) 4 <===answer

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