Question

point y is in the interior of $\angle xwz$. given that $\overrightarrow{wx}$ and $\overrightarrow{wz}$ are opposite rays and $m\angle xwy = 4m\angle ywz$, what is $m\angle ywz$?

$m\angle ywz = \square$
(simplify your answer. do not include the degree symbol in your answer.)

Explanation:

Step1: Identify the straight angle

Since \(\overrightarrow{WX}\) and \(\overrightarrow{WZ}\) are opposite rays, \(\angle XWZ = 180^\circ\). Let \(m\angle YWZ=x\), then \(m\angle XWY = 4x\).

Step2: Set up the equation

We know that \(m\angle XWY + m\angle YWZ=m\angle XWZ\). Substituting the values, we get \(4x + x=180\).

Step3: Solve the equation

Combining like terms, \(5x = 180\). Dividing both sides by 5, \(x=\frac{180}{5}=36\).

Answer:

36