Question

in the given figure, x = 30°. whats the property of parallel lines used to find x?
a) corresponding angles are congruent.
b) angles at the same side of the transversal are supplementary.
c) alternate interior angles are congruent.
d) alternate exterior angles are congruent.

Explanation:

1. Recall the definitions of angle properties for parallel lines cut by a transversal:

• Corresponding angles (A) are in the same position relative to the parallel lines and transversal.
• Same - side angles (B) add up to 180°.
• Alternate interior angles (C) are inside the parallel lines and on alternate sides of the transversal.
• Alternate exterior angles (D) are outside the parallel lines and on alternate sides of the transversal.

1. In the given figure, the 30° angle and angle \(x\) are outside the two parallel lines (\(p\) and \(q\)) and on alternate sides of the transversal \(r\). So, the property used is that alternate exterior angles are congruent.

Answer:

D) Alternate exterior angles are congruent.