Question

two parallel lines, a and b, are cut by transversal p. what is the measure of ∠x if ∠y = 23? a 65° b 75° c 105° d 157

Explanation:

Step1: Recall angle - relationship

When two parallel lines are cut by a transversal, corresponding angles are congruent and adjacent angles are supplementary. ∠X and ∠Y are adjacent angles (linear - pair), and the sum of angles in a linear - pair is 180°.

Step2: Calculate the measure of ∠X

Let \(m\angle X=x\) and \(m\angle Y = 23^{\circ}\). We know that \(x+23^{\circ}=180^{\circ}\). Solving for \(x\), we get \(x = 180^{\circ}-23^{\circ}\).
\[x=157^{\circ}\]

Answer:

D. \(157^{\circ}\)