Question

HELP ME ASAP

In the following diagram overline DE || overline FG and overline KL perp FG. What is the measure of angle x?

Angle x = _____°​

Answer 1

Given:

DE||FG and KL is perpendicular to FG.

To find:

The measure of angle x.

Solution:

If two lies intersect each other, then vertical opposite angles are equal.

`m\angle ACB=63^\circ` (Vertically opposite angles)

`m\angle BAC=x^\circ` (Vertically opposite angles)

KL is perpendicular to FG.

`m\angle ABC=90^\circ`

According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees.

In triangle ABC,

`m\angle ABC+m\angle BAC+m\angle ACB=180^\circ`

`90^\circ+x^\circ+63^\circ=180^\circ`

`x^\circ+153^\circ=180^\circ`

`x^\circ=180^\circ-153^\circ`

`x^\circ=27^\circ`

Therefore, the measure of angle x is 27 degrees.