Video: Finding the Measure of an Unknown Angle Using the Properties of Parallelograms

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.