Question

A pair of parallel lines is cut by a transversal:

What is the measure of angle x?
50 degrees
55 degrees
60 degrees
80 degrees

Answer 1

60 degrees.

Angle x°+25° and angle 85° are alternate interior angles, therefore they are congruent.

85 - 25 = 60°

Answer 2

Answer: 60 degrees

Explanation:

We know that when a traversal line passes through two parallel lines , then the alternate interior angles are equal ( or congruent). (1)

From the given picture,we have two parallel line intersecting by a transversal line, making a pair of alternate interior angles as x+25° and 85°. (2)

From (1) and (2), we have

`x+25^(\circ)=85^(\circ)`

Subtract
`25^(\circ)` from both the sides , we get

`x=85^(\circ)-25^(\circ)=60^(\circ)`

Hence, the measure of angle x = 60 degrees