Video Transcript
Find the measure of angle
𝐹𝐺𝐸.
The diagram shows a parallelogram,
where lines 𝐸𝐹 and 𝐺𝐻 are parallel. The sides 𝐸𝐻 and 𝐹𝐺 are also
parallel. We can therefore use our angle
properties involving parallel lines to find the measure of angle 𝐹𝐺𝐸. We begin by recalling that
alternate angles are congruent. These are often referred to as
“zed” or “zee” angles. In this question, angle 𝐻𝐺𝐸 is
equal to angle 𝐺𝐸𝐹. They are both equal to 31
degrees.
𝐸𝐹𝐺 is a triangle. And we know that angles in a
triangle sum to 180 degrees. This means that 𝑥 plus 31 plus 106
is equal to 180. Simplifying this gives us 𝑥 plus
137 is equal to 180. Finally, subtracting 137 from both
sides gives us 𝑥 equals 43. We can therefore conclude that the
measure of angle 𝐹𝐺𝐸 is equal to 43 degrees.
