Question

question 11
find m∠yxz.
© algebra einstein, 2023

Explanation:

Step1: Set the angles equal

Since vertical - angles are equal, we set \(7x + 8=4x+30.5\).
\[7x + 8=4x+30.5\]

Step2: Solve for x

Subtract \(4x\) from both sides: \(7x-4x + 8=4x-4x+30.5\), which simplifies to \(3x+8 = 30.5\). Then subtract 8 from both sides: \(3x+8 - 8=30.5 - 8\), getting \(3x=22.5\). Divide both sides by 3: \(x=\frac{22.5}{3}=7.5\).

Step3: Find the measure of \(\angle YXZ\)

Substitute \(x = 7.5\) into the expression for \(\angle YXZ\) which is \(4x+30.5\). So \(m\angle YXZ=4\times7.5 + 30.5\). First, \(4\times7.5 = 30\), then \(30+30.5=60.5\).

Answer:

\(60.5^{\circ}\)