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.
[tex]m\angle ACB=63^\circ [/tex] (Vertically opposite angles)
[tex]m\angle BAC=x^\circ [/tex] (Vertically opposite angles)
KL is perpendicular to FG.
[tex]m\angle ABC=90^\circ[/tex]
According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees.
In triangle ABC,
[tex]m\angle ABC+m\angle BAC+m\angle ACB=180^\circ[/tex]
[tex]90^\circ+x^\circ+63^\circ=180^\circ[/tex]
[tex]x^\circ+153^\circ=180^\circ[/tex]
[tex]x^\circ=180^\circ-153^\circ[/tex]
[tex]x^\circ=27^\circ[/tex]
Therefore, the measure of angle x is 27 degrees.
