Question

find the measure of ∠bpk.

Explanation:

Step1: Set up the equation

Vertical - angles are equal. So, \(4m + 99=7m+108\).

Step2: Solve for \(m\)

Subtract \(4m\) from both sides: \(99 = 3m+108\). Then subtract 108 from both sides: \(3m=99 - 108=-9\). Divide both sides by 3: \(m=- 3\).

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

Substitute \(m = - 3\) into the expression for \(\angle BPK\) which is \(7m + 108\). So, \(7(-3)+108=-21 + 108 = 87\).

Answer:

\(87\)