Question

What is the measure of angle x? A pair of parallel lines is cut by a transversal. An exterior angle on the left of the transversal is labeled as 50 degrees. An interior angle on the right of the transversal, which is not vertically opposite to the 50 degree angle, is labeled as x. 100 degrees 130 degrees 135 degrees 150 degrees

Answer 1

The sum of consecutive interior angles is 180. Also called same side interior angles.
If the 50 degree exterior angle is brought interior by vertical angle thm and it becomes same side interior to x, then x is 130 degrees.

Answer 2

The measure of angle x=
`130^(\circ)`.

Explanation:

We are given that a pair of parallel lines is cut by a transversal line .

Let a pair of parallel lines are AB and EF and the transversal line CD cut the parallel lines AB and EF.

We are given that an exterior angle on the left side of the transversal line is 50 degrees.

The interior angle on the right side of transversal line is x which is not vertical opposite to exterior angle =50 degrees

We know that when two lines are parallel and cut by a transversal line then corresponding angles are congruent.

Therefore,exterior angle=
`\angle FDC=50^(\circ)`

We know that linear pair sum=
`180^(\circ)`

`\angle FDC+\angle CDE=180^(\circ)`

`50+\angle` CDE=180

substitute the value

`\angle` CDE=180-50

By subtraction property of equality

`\angle CDE=x=130^(\circ)`.

Hence, the measure of angle x=
`130^(\circ)`.Therefore, option B is correct.