Find the measure of each angle indicated.
A) 75°
C) 67°
B) 114 °
D) 107°

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Explanation:

Refer to the diagram below. I've added the variables x, y and z. The goal is to find x. For now, let's find y.

Focus on the larger triangle. The three angles of any triangle must add to 180.

46+64+y = 180

110+y = 180

y = 180-110

y = 70

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Next, we'll find the angle z

The three angles y = 70, 49, and z all form a straight angle of 180 degrees.

y+49+z = 180

70+49+z = 180

119+z = 180

z = 180-119

z = 61

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Now we can find angle x. Focus on the smaller triangle

z+52+x = 180

61+52+x = 180

113+x = 180

x = 180-113

x = 67 which points us to choice C as the final answer.

step-by-step explanation: