Question

find the measure of \\( \angle m p f \\).

Explanation:

Step1: Set up the equation

Since \( \angle HPF=\angle FPM\), we have \(8b - 14=2b + 14\).

Step2: Solve for \(b\)

Subtract \(2b\) from both sides: \(8b-2b - 14=2b-2b + 14\), so \(6b-14 = 14\).
Add \(14\) to both sides: \(6b-14 + 14=14 + 14\), then \(6b=28\), and \(b=\frac{28}{6}=\frac{14}{3}\).

Step3: Find \( \angle MPF\)

Substitute \(b = \frac{14}{3}\) into \(2b + 14\).
\(2\times\frac{14}{3}+14=\frac{28}{3}+\frac{42}{3}=\frac{28 + 42}{3}=\frac{70}{3}\approx23.33^{\circ}\).

Answer:

\(\frac{70}{3}\) (or approximately \(23.33^{\circ}\))