Question

1. m∠def______

Explanation:

Step1: Use the property of alternate interior angles

Since the two lines are parallel, the alternate interior angles are equal. So, \(8x - 34=5x + 2\).

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides: \(8x-5x - 34=5x-5x + 2\), which simplifies to \(3x-34 = 2\).
Add \(34\) to both sides: \(3x-34 + 34=2 + 34\), getting \(3x=36\).
Divide both sides by \(3\): \(x = 12\).

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

Substitute \(x = 12\) into \(5x + 2\). So, \(5\times12+2=60 + 2=62\).

Answer:

\(62^{\circ}\)