Question

point y is in the interior of ∠xwz. given that \\(\overleftrightarrow{wx}\\) and \\(\overleftrightarrow{wz}\\) are opposite rays and \\(m\angle xwy = 4(m\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: Determine the straight angle

Since \(\overrightarrow{WX}\) and \(\overrightarrow{WZ}\) are opposite rays, \(\angle XWZ\) is a straight angle, so \(m\angle XWZ = 180\).

Step2: Set up the angle addition equation

Let \(m\angle YWZ = x\). Then \(m\angle XWY = 4x\) (given \(m\angle XWY = 4(m\angle YWZ)\)). By the angle addition postulate, \(m\angle XWY + m\angle YWZ = m\angle XWZ\). Substituting the values, we get \(4x + x = 180\).

Step3: Solve the equation

Combine like terms: \(5x = 180\). Divide both sides by 5: \(x=\frac{180}{5}=36\).

Answer:

36