Question

(c) problem 18: (first taught in lesson 31) using this diagram, find y in terms of z. then, select your answer.

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In \(\triangle RSV\), the exterior angle \(\angle STV = 2y^{\circ}\), and the two non - adjacent interior angles are \(y^{\circ}\) and \(\angle SVT\). In \(\triangle SUV\), \(\angle SVT\) is an exterior angle. By the exterior angle theorem, \(\angle SVT=z^{\circ}+4z^{\circ}=5z^{\circ}\).

Step2: Set up the equation

Since \(\angle STV\) (which is \(2y^{\circ}\)) is the exterior angle of \(\triangle RSV\) with non - adjacent interior angles \(y^{\circ}\) and \(\angle SVT = 5z^{\circ}\), we have the equation \(2y=y + 5z\).

Step3: Solve the equation for \(y\)

Subtract \(y\) from both sides of the equation \(2y=y + 5z\).

$$2y-y=y + 5z-y$$

$$y = 5z$$

Answer:

\(y = 5z\)