Question

15 in the following diagram, the lines ab and pq are parallel to each other and tt is the transversal that cut the parallel lines. what is the value of the unknown x?

Explanation:

Step1: Find the measure of the angle adjacent to \(112^{\circ}\)

Since the sum of adjacent angles on a straight line is \(180^{\circ}\), the angle adjacent to \(112^{\circ}\) is \(180 - 112=68^{\circ}\).

Step2: Use the property of parallel lines and transversal

When two parallel lines \(AB\) and \(PQ\) are cut by a transversal \(TT'\), the corresponding angles are equal. So \(3x - 25=68\).

Step3: Solve the equation for \(x\)

Add \(25\) to both sides of the equation: \(3x=68 + 25\), so \(3x=93\).
Divide both sides by \(3\): \(x=\frac{93}{3}\).

Answer:

\(31\)