In the given figure if PQ ∥ RS, then the value of x is–

To solve for the value of x in the given figure, we must use the geometric property that when two parallel lines are cut by a transversal, the consecutive interior angles (also known as co-interior angles) are supplementary, meaning their sum is 180°.

Step-by-Step Solution
Identify the relationship: Based on the figure, the angles labeled (3x - 20)° and (2x - 10)° are consecutive interior angles between the parallel lines PQ and RS.

Set up the equation: Since these angles are supplementary:
(3x - 20) + (2x - 10) = 180

Combine like terms:
(3x + 2x) + (-20 - 10) = 180
5x - 30 = 180

Solve for x:

Add 30 to both sides: 5x = 210

Divide by 5: x = 210 / 5

x = 42