Question

1. use structure given $ellparallel m$ and $aparallel b$. what are the values of $x$, $y$, and $z$?

(a) $x = 105$, $y = 105$, and $z = 85$
(b) $x = 95$, $y = 95$, and $z = 85$
(c) $x = 85$, $y = 85$, and $z = 105$
(d) $x = 85$, $y = 85$, and $z = 95$

Explanation:

Step1: Use parallel - line angle properties

When two parallel lines are cut by a transversal, corresponding angles are equal and alternate - interior angles are equal. Assume there is an angle related to \(x\) and \(y\) which is equal to them due to parallel lines \(\ell\parallel m\) and \(a\parallel b\). Also, if we consider a linear - pair relationship for \(z\) with an angle related to \(x\) or \(y\). Let's assume the angle corresponding to \(x\) and \(y\) is \(85^{\circ}\), so \(x = 85^{\circ}\) and \(y=85^{\circ}\) because of corresponding or alternate - interior angles.

Step2: Calculate \(z\)

Since \(z\) and the angle equal to \(x\) and \(y\) form a linear pair (sum of angles on a straight line is \(180^{\circ}\)), if the angle equal to \(x\) and \(y\) is \(85^{\circ}\), then \(z=180 - 85=95^{\circ}\).

Answer:

D. \(x = 85,y = 85\), and \(z = 95\)