In the figure below, lines a and b are parallel, and lines c and d are parallel.
What is the measure of ∠x ?
Just one way to look at it is:
The missing angle in the triangle containing the angles of 30° and 75° is equal to 75°,
since angles of a triangle add up to 180°
Therefore, since lines a and b are parallel, and lines c and d are also parallel,
the angle to the right of ∠x is also equal to 75°. A parallelogram is formed, where opposite angles are equal.
Angles in a straight line add up to 180°. Since the angle to the right of ∠x is 75°,
then ∠x is equal to 105°.
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