Question

10 in the following diagram, the lines ab and pq are parallel to each other an what is the value of the unknown x? you must show your on the paper provided to receive credit.

Explanation:

Step1: Identify angle - relationship

Since AB and PQ are parallel, the angle \(112^{\circ}\) and the angle \((3x - 25)^{\circ}\) are corresponding angles, so they are equal.
\[3x-25 = 112\]

Step2: Solve the equation for \(x\)

Add 25 to both sides of the equation:
\[3x=112 + 25\]
\[3x=137\]
Then divide both sides by 3:
\[x=\frac{137}{3}\]

Answer:

\(x = \frac{137}{3}\)