Question

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Triangle DOG is similar to triangle CAT. In triangle CAT, angle C is 81 degrees and angle A is 67 degrees. Determine the measure of angle G.
A. 148 degrees
B. 81 degrees
C. 67 degrees
D. 32 degrees

Answer 1

D. 32 degrees

Explanation:

First you must know that the sum of angle in a triangle is 180. Hence in triangle CAG;

<C + <A+ <T = 180

Given

<C = 81 degrees

<A = 67 degrees

Substitute

Get <T first

81 + 67 + <T = 180

148 + <T = 180

<T = 180 - 148

<T = 32 degrees

Since Triangle DOG is similar to triangle CAT, then <T = <G = 32 degrees

Hence the measure of <G is 32 degrees