Question

1. find the value of x. then find the measure of each labeled angle.

x = 20; the labeled angles are 160° and 20°.

x = 110; the labeled angles are 110° and 70°.

x = 20; the labeled angles are 60° and 20°.

x = 70; the labeled angles are 110° and 70°.

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. So, \(x+(x + 40)=180\).

Step2: Solve the equation for \(x\)

Expand the left - hand side: \(x+x + 40=180\), which simplifies to \(2x+40 = 180\).
Subtract 40 from both sides: \(2x=180 - 40\), so \(2x=140\).
Divide both sides by 2: \(x=\frac{140}{2}=70\).

Step3: Find the measure of the other angle

Substitute \(x = 70\) into \(x + 40\): \(70+40 = 110\).

Answer:

\(x = 70\); the labeled angles are \(110^{\circ}\) and \(70^{\circ}\) (the fourth option).