Question

find the measure of ∠gjk. m∠gjk =

Explanation:

Step1: Use vertical - angle property

Since $\angle GJK$ and the angle with measure $(3x + 63)^{\circ}$ are vertical angles, they are equal. So we set up the equation $2x+92 = 3x + 63$.

Step2: Solve for $x$

Subtract $2x$ from both sides: $92=x + 63$. Then subtract 63 from both sides: $x=92 - 63=29$.

Step3: Find the measure of $\angle GJK$

Substitute $x = 29$ into the expression for $\angle GJK$ which is $2x+92$. So $m\angle GJK=2\times29 + 92$. First, calculate $2\times29 = 58$. Then $58+92 = 150$.

Answer:

$150$