Question

name:
lines m and p are parallel and cut by transversal t in this figure.
what is the value of x?

Explanation:

Step1: Find the supplementary angle of \(120^{\circ}\)

When two angles are supplementary, their sum is \(180^{\circ}\). Let the supplementary angle of \(120^{\circ}\) be \(y\). Then \(y = 180^{\circ}- 120^{\circ}=60^{\circ}\)

Step2: Use the property of parallel lines and transversal

Since \(m\parallel p\), we know that the sum of the angles \(x\), \(y\) (from step 1) and \(50^{\circ}\) (corresponding angle property) forms a straight - line - like relationship (using the concept of alternate - interior angles and angle addition).
We know that \(x + y+50^{\circ}=180^{\circ}\) (sum of angles on a straight line). Substitute \(y = 60^{\circ}\) into the equation: \(x+60^{\circ}+50^{\circ}=180^{\circ}\)

Step3: Solve for \(x\)

\(x=180^{\circ}-(60^{\circ} + 50^{\circ})\)
\(x=180^{\circ}-110^{\circ}\)
\(x = 70^{\circ}\)

Answer:

\(70\)