Answer:
x = 108°
Explanation:
You want the measure of the angle marked x in the given figure where parallel lines cut through a triangle.
Angle sum
The angle sum theorem tells you the angle at lower left will have the value that makes the sum of angles in the larger triangle equal to 180°.
lower left angle = 180° -77° -36° = 67°
Corresponding angles
Then the exterior angle of the smallest triangle, marked y in the attachment, will be the sum of the remote interior angles 67° and 41°:
y = 67° +41° = 108°
Angle y is a corresponding angle to angle x, so has the same measure.
x = 108°
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Additional comment
The angles in the attachment are drawn accurately.
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