In the figure below, lines

What is the measure of ∠

*a*and*b*are parallel, and lines*c*and*d*are parallel.What is the measure of ∠

*x*?
A.) 75°

B.) 95°

C.) 100°

D..) 105°

E.) 113°

B.) 95°

C.) 100°

D..) 105°

E.) 113°

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

the angle to the right of ∠

Angles in a straight line add up to 180°. Since the angle to the right of ∠

then ∠

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°.**D.) 105°**

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