Question

1. find m ∠ bfh

type a response
m||n

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), the angles \((5x + 22)\) and \((7x-14)\) are alternate - interior angles, and alternate - interior angles are equal. So we set up the equation \(5x + 22=7x - 14\).

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides: \(22 = 7x-5x - 14\), which simplifies to \(22 = 2x-14\). Then add 14 to both sides: \(22 + 14=2x\), so \(36 = 2x\). Divide both sides by 2: \(x = 18\).

Step3: Find the measure of one of the angles

Substitute \(x = 18\) into \(5x + 22\): \(5\times18+22=90 + 22=112\).

Step4: Find \(\angle BFH\)

\(\angle BFH\) and the angle \((5x + 22)\) are supplementary (linear - pair of angles). Let \(m\angle BFH=y\). Then \(y+(5x + 22)=180\). Since \(5x + 22 = 112\), then \(y=180 - 112 = 68\).

Answer:

\(68\)