Answer: Choice C) 67 degrees
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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.
