Question

What is the value of x which proves that the runways are parallel? What is the measure of the larger angle?

A) x = 20; 92 degrees
B) x = 40; 88 degrees
C) x = 25; 107 degrees
D) x = 30; 115 degrees

Answer 1

The answer is C) x = 25; 107 degrees

Answer 2

The correct option is C.

Explanation:

if a transversal line intersect two parallel lines then the sum of two consecutive exterior angles is 180 degrees.

The two consecutive exterior angles are 3x+32 and x+48.

`3x+32+x+48=180`

`4x+80=180`

`4x=180-80`

`4x=100`

`x=25`

The value of x is 25.

The measure of two consecutive exterior angles are

`3x+32=3(25)+32=107`

`x+48=25+48=73`

The measure of the larger angle is 107 degrees.

Therefore the correct option is C.