Question

find the measure of ∠bph.

Explanation:

Step1: Use the linear - pair relationship

Angles that form a linear pair are supplementary. That is, if two angles form a linear pair, the sum of their measures is \(180^{\circ}\). In this case, \(\angle BPD\) and \(\angle BPH\) form a linear pair. So, \(\angle BPD+\angle BPH = 180^{\circ}\).

Step2: Substitute the known value

We know that \(\angle BPD = 111^{\circ}\). Substituting this value into the equation \(\angle BPD+\angle BPH=180^{\circ}\), we get \(111^{\circ}+\angle BPH = 180^{\circ}\).

Step3: Solve for \(\angle BPH\)

To find \(\angle BPH\), we use the subtraction property of equality. \(\angle BPH=180^{\circ}- 111^{\circ}\).

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Answer:

\(69^{\circ}\)