Question

m∠xyz = 117°
find m∠xyw and m∠wyz.
(6x + 44)° (-10x + 65)°
m∠xyw =
°
m∠wyz =
°

Explanation:

Step1: Set up equation

Since \(m\angle XYZ=m\angle XYW + m\angle WYZ\), we have \((6x + 44)+(-10x + 65)=117\).

Step2: Combine like - terms

\[

$$\begin{align*} 6x-10x+44 + 65&=117\\ -4x+109&=117 \end{align*}$$

\]

Step3: Solve for \(x\)

Subtract 109 from both sides: \(-4x=117 - 109=8\). Then divide both sides by - 4, so \(x=-2\).

Step4: Find \(m\angle XYW\)

Substitute \(x = - 2\) into the expression for \(m\angle XYW\): \(m\angle XYW=6x + 44=6\times(-2)+44=-12 + 44 = 32^{\circ}\).

Step5: Find \(m\angle WYZ\)

Substitute \(x=-2\) into the expression for \(m\angle WYZ\): \(m\angle WYZ=-10x + 65=-10\times(-2)+65=20 + 65 = 85^{\circ}\).

Answer:

\(m\angle XYW = 32^{\circ}\), \(m\angle WYZ = 85^{\circ}\)