Answers:
x = 13
Question mark angle is 64 degrees
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Step-by-step explanation:
Let y be the angle labeled as a question mark.
This angle y is adjacent to the exterior angle of measure 116 degrees
This means y and 116 must add to 180 to form a straight angle
y+116 = 180
y = 180-116
y = 64
So 64 degrees will replace the question mark.
Then we can find the angle x. Recall that all angles of a triangle add to 180
90+2x+y = 180
90+2x+64 = 180
2x+154 = 180
2x = 180-154
2x = 26
x = 26/2
x = 13
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Alternatively, you can find x through the remote interior angle theorem
The interior angles 90 and 2x add to the exterior angle 116
90+2x = 116
2x = 116-90
2x = 26
x = 26/2
x = 13
This method doesn't involve angle y.