Question

1. in the adjoining figure, pq intersects a pair of parallel lines ab and mn at... (a) write the name of a pair of alternate interior angles from the figure (b) find the value of x. ( x + 60^circ + 2x = 180^circ ) (being adjacent angles?)

Explanation:

Step1: Identify the angle relationship

Since \( PQ \parallel MN \) and a transversal intersects them, the given angle \( 110^\circ \) and the angle adjacent to \( x \) (let's say \( \angle A \)) are supplementary? Wait, no, looking at the solution steps provided (from the handwritten note: \( x + 110^\circ = 180^\circ \) because they are adjacent angles on a straight line? Wait, maybe alternate interior angles or consecutive interior angles. Wait, the handwritten step says "being adjacent angles" (probably consecutive interior angles or linear pair? Wait, the equation is \( x + 110^\circ = 180^\circ \), so they are supplementary (linear pair or consecutive interior angles). So we set up the equation.

Step2: Solve for \( x \)

Given \( x + 110^\circ = 180^\circ \), subtract \( 110^\circ \) from both sides:
\( x = 180^\circ - 110^\circ \)
\( x = 70^\circ \)

Answer:

\( x = 70^\circ \)