Question

find the measure of ∠gjk.

m∠gjk = \boxed{}°

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Explanation:

Step1: Use the property of corresponding angles

Since \(FG\parallel HI\), \(\angle GJK\) and \((3x + 63)^{\circ}\) are corresponding angles. So \(2x+92 = 3x + 63\).

Step2: Solve the equation for \(x\)

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

Step3: Calculate the measure of \(\angle GJK\)

Substitute \(x = 29\) into \(2x+92\).
\(2\times29+92=58 + 92=150\).

Answer:

\(150\)