1 Answer

Duncmc · Answer 1 · 2022-09-16T17:20:51+0000

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.

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