Question

find the measure of ∠bhc.

Explanation:

Step1: Set up an equation

Since $\angle GHC+\angle BHC = 90^{\circ}$ (right - angle), we have $(7p + 15)+(6p-3)=90$.

Step2: Combine like - terms

Combining the $p$ terms and the constant terms, we get $7p+6p+15 - 3=90$, which simplifies to $13p + 12=90$.

Step3: Solve for $p$

Subtract 12 from both sides: $13p=90 - 12=78$. Then divide both sides by 13, so $p = \frac{78}{13}=6$.

Step4: Find the measure of $\angle BHC$

Substitute $p = 6$ into the expression for $\angle BHC$ which is $6p-3$. So $\angle BHC=6\times6 - 3=36 - 3=33^{\circ}$.

Answer:

$33^{\circ}$