Video Transcript
From the figure, determine the
measure of angle 𝐵𝐸𝐷.
Angle 𝐵𝐸𝐷 is this one. Let’s define it to be equal to 𝑥
degrees. Then, we recall what we actually
know about angles in quadrilaterals. Remember, that’s a four-sided
polygon. We know that the interior angles in
a quadrilateral sum to make 360 degrees. Well, we have a quadrilateral
𝐵𝐶𝐷𝐸. And we know one of its angles is
148 degrees and another is 90. The problem is we can’t find the
measure of 𝐵𝐸𝐷 without knowing a third angle. That’s this one. Let’s call that 𝑦 degrees.
We can work out the measure of
angle 𝑦 or angle 𝐶𝐵𝐸. We know that angles on a straight
line sum to 180 degrees. We see that angle 𝐴𝐵𝐸 is 100
degrees. So 100 plus 𝑦 must be equal to
180. Let’s solve this equation for 𝑦 by
subtracting 100 from both sides. And we see that 𝑦 is 180 minus
100, which is 80. So we now know a third interior
angle in our quadrilateral. Let’s use this information to form
an equation.
The interior angle sum of our
quadrilateral is 80 plus 90 plus 148 plus 𝑥, which is equal to 360. 80 plus 90 plus 148 is 318. So our equation is 318 plus 𝑥
equals 360. We’ll solve this equation for 𝑥 by
subtracting 318 from both sides. 360 minus 318 is 42. So we find 𝑥 is equal to 42. We therefore say that the measure
of angle 𝐵𝐸𝐷 is 42 degrees.
