Question

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

Explanation:

Step1: Use the property of consecutive - interior angles

Since \(EF\parallel GH\), the sum of \((4x)^{\circ}\) and \((12x - 12)^{\circ}\) is \(180^{\circ}\) (consecutive - interior angles are supplementary).
So, \(4x+(12x - 12)=180\).

Step2: Solve the equation for \(x\)

Combine like terms: \(4x+12x-12 = 180\), which simplifies to \(16x-12 = 180\).
Add \(12\) to both sides: \(16x=180 + 12\), so \(16x=192\).
Divide both sides by \(16\): \(x=\frac{192}{16}=12\).

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

Substitute \(x = 12\) into the expression for \(\angle GJI=(12x - 12)^{\circ}\).
\(12x-12=12\times12-12\).
First, calculate \(12\times12 = 144\), then \(144-12=132\).

Answer:

\(132\)