Question

A pair of parallel lines is cut by a transversal:

A pair of parallel lines is cut by a transversal. The interior angle made on the left by the intersection of the upper parallel line and the transversal is divided into 2 parts by a slanting line. One part of this angle is labeled as x, and the other part is labeled as 30 degrees. The interior angle made on the right by the intersection of the lower parallel line and the transversal is labeled as 75 degrees.

What is the measure of angle x?

Answer 1

it is 45 degrees dude, really

Answer 2

x = 45°

Explanation:

It a transversal line intersect two parallel lines, then alternative interior angles are congruent.

From the below graph it is clear that the line m and n are two parallel lines and l is a transversal line.

`\angle ABC\cong \angle BCD` (Alternative interior angles)

`m\angle ABC=m\angle BCD` (Definition of congruent angles)

`x+30^(\circ)=75^(\circ)`

Subtract 30° from both sides.

`x+30^(\circ)-30^(\circ)=75^(\circ)-30^(\circ)`

`x=45^(\circ)`

Therefore the measure of angle x is 45°.