Question

find ( mangle klj ) (hint: they are corresponding angles).

( mangle klj = )

Explanation:

Step1: Set up the equation

Since \( \angle G\) and \( \angle KLJ\) are corresponding angles and \( K\) is the mid - point of \( HJ\) and \( L\) is the mid - point of \( GJ\) (by the mid - segment theorem in a triangle, \( KL\parallel HG\)), so \(5x - 2=9x - 62\).

Step2: Solve for \(x\)

Subtract \(5x\) from both sides:
\(-2 = 4x-62\)
Add \(62\) to both sides:
\(60 = 4x\)
Divide both sides by \(4\):
\(x = 15\)

Step3: Find \(m\angle KLJ\)

Substitute \(x = 15\) into \(9x - 62\):
\(9\times15-62=135 - 62\)

Answer:

\(73^{\circ}\)