Question

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

Explanation:

Step1: Identify angle - relationship

Since lines AB and PQ are parallel and TT is a transversal, the angle (6x - 25)° and the 112° angle are corresponding angles. Corresponding angles formed by a transversal cutting two parallel lines are equal. So, we set up the equation 6x−25 = 112.

Step2: Solve the equation for x

Add 25 to both sides of the equation: 6x−25 + 25=112 + 25, which simplifies to 6x=137. Then divide both sides by 6: x = $\frac{137}{6}$=22.83 (rounded to two - decimal places).

Answer:

x = $\frac{137}{6}\approx22.83$