Question

find the measure of ∠cgm.

Explanation:

Step1: Set up equation

Since $\angle YGC$ and $\angle CGM$ are supplementary (linear - pair of angles), their sum is $180^{\circ}$. So, $(7h + 84)+(4h-3)=180$.

Step2: Combine like - terms

Combining the $h$ terms and the constant terms, we get $7h+4h + 84 - 3=180$, which simplifies to $11h+81 = 180$.

Step3: Solve for $h$

Subtract 81 from both sides: $11h=180 - 81$, so $11h=99$. Then divide both sides by 11: $h=\frac{99}{11}=9$.

Step4: Find $\angle CGM$

Substitute $h = 9$ into the expression for $\angle CGM$ which is $4h-3$. So, $\angle CGM=4\times9-3=36 - 3=33^{\circ}$.

Answer:

$33^{\circ}$