Question

question 8
note: figure not drawn to scale.
in the figure shown, line c intersects parallel lines s and t. what is the value of x?

Explanation:

Step1: Identify angle - relationship

When a transversal intersects two parallel lines, corresponding angles are equal. Here, the angle of 110° and the angle adjacent to \(x\) are corresponding angles, so the angle adjacent to \(x\) is 110°.

Step2: Use linear - pair property

Since \(x\) and the 110° - adjacent angle form a linear pair (sum of angles on a straight - line is 180°), we have \(x + 110^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Subtract 110° from both sides of the equation: \(x=180^{\circ}-110^{\circ}\).

Answer:

\(x = 70^{\circ}\)