Question

find the measure of ∠bgr.

Explanation:

Step1: Set up equation

Since the sum of angles on a straight - line is 180 degrees, we have $(4t + 98)+(7t-28)=180$.

Step2: Combine like terms

$4t+7t+98 - 28=180$, which simplifies to $11t + 70=180$.

Step3: Solve for t

Subtract 70 from both sides: $11t=180 - 70=110$. Then divide both sides by 11, so $t = 10$.

Step4: Find measure of ∠BGR

Substitute $t = 10$ into the expression for ∠BGR which is $7t-28$. So $7\times10-28=70 - 28=42$.

Answer:

$42^{\circ}$