Question

find the measure of \\( \angle g j k \\).
\\( m \angle g j k = \\) \\( \circ \\)
submit

Explanation:

Step1: Use the property of corresponding angles

Since \(FG\parallel HI\), \(\angle GJK\) and \(\angle JKI\) are same - side interior angles. The sum of same - side interior angles is \(180^{\circ}\). So, \((2x + 92)+(3x + 63)=180\).

Step2: Solve the equation for \(x\)

Combine like terms: \(2x+3x+92 + 63=180\), which simplifies to \(5x+155 = 180\).
Subtract \(155\) from both sides: \(5x=180 - 155\), so \(5x=25\).
Divide both sides by \(5\): \(x = 5\).

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

Substitute \(x = 5\) into the expression for \(\angle GJK\) (\(2x + 92\)).
\(2x+92=2\times5+92\).
First, calculate \(2\times5 = 10\). Then \(10+92=102\).

Answer:

\(102\)