Question

find the measure of ∠bph.

Explanation:

Step1: Use the definition of a linear pair

A linear pair of angles is supplementary (sum to \(180^{\circ}\)). \(\angle BPH\) and the \(111^{\circ}\) angle form a linear pair.
Let \(m\angle BPH=x\). Then \(x + 111^{\circ}=180^{\circ}\).

Step2: Solve for \(x\)

Subtract \(111^{\circ}\) from both sides of the equation: \(x=180^{\circ}- 111^{\circ}\).

$$x = 69^{\circ}$$

Answer:

\(69^{\circ}\)