Video Transcript
Find the measure of angle
๐น๐บ๐ธ.
The diagram shows a parallelogram,
where lines ๐ธ๐น and ๐บ๐ป are parallel. The sides ๐ธ๐ป and ๐น๐บ are also
parallel. We can therefore use our angle
properties involving parallel lines to find the measure of angle ๐น๐บ๐ธ. We begin by recalling that
alternate angles are congruent. These are often referred to as
โzedโ or โzeeโ angles. In this question, angle ๐ป๐บ๐ธ is
equal to angle ๐บ๐ธ๐น. They are both equal to 31
degrees.
๐ธ๐น๐บ is a triangle. And we know that angles in a
triangle sum to 180 degrees. This means that ๐ฅ plus 31 plus 106
is equal to 180. Simplifying this gives us ๐ฅ plus
137 is equal to 180. Finally, subtracting 137 from both
sides gives us ๐ฅ equals 43. We can therefore conclude that the
measure of angle ๐น๐บ๐ธ is equal to 43 degrees.
