Question

(c) problem 20: (first taught in lesson 53) in \\( \square stuv \\), find \\( y \\) in terms of \\( x \\) and \\( z \\). after you pick your answer press go. a. \\( y = 180 - z - x \\) b. \\( y = x - z \\) c. \\( y = z + x \\) d. \\( y = z - x \\) e. \\( y = -x - z \\)

Explanation:

Step1: Use the property of parallelogram

In parallelogram \(STUV\), \(ST\parallel UV\). Let's consider the transversal.

Step2: Use the property of alternate - interior angles

Since \(ST\parallel UV\), the angle adjacent to \(y\) (let's call it \(\angle1\)) and the angle with measure \((x + z)\) are equal (because of the property of parallel lines and transversal: if two parallel lines are cut by a transversal, then the alternate - interior angles are equal). And we know that \(y+\angle1 = 180^{\circ}\) (linear pair). So \(y=180-(x + z)\)

Answer:

A. \(y = 180 - z - x\)