Video Transcript
Given that the measure of angle
𝐵𝐴𝐷 is equal to 36 degrees and the measure of angle 𝐶𝐵𝐴 is equal to 37
degrees, find the measure of angle 𝐵𝐶𝐷 and the measure of angle 𝐶𝐷𝐴.
Let’s begin by adding the angles
that we know onto the diagram. The measure of angle 𝐵𝐴𝐷 is
equal to 36 degrees, and the measure of angle 𝐶𝐵𝐴 is equal to 37. We are looking to calculate the
measure of angle 𝐵𝐶𝐷, which is this one, and the measure of angle 𝐶𝐷𝐴, which
is this one. We now observe that the first
unknown angle, that’s 𝐵𝐶𝐷, is subtended by the same arc 𝐵𝐷 as angle 𝐵𝐴𝐷. And we know that inscribed angles
subtended by the same arc are equal. So the measure of angle 𝐵𝐴𝐷 must
be equal to the measure of angle 𝐵𝐶𝐷. But of course, we’ve now seen that
that’s 36 degrees.
In a similar way, we observed that
angle 𝐴𝐷𝐶 is subtended from the same arc as angle 𝐴𝐵𝐶. And so, these two angles are
congruent. The measure of angle 𝐴𝐵𝐶 must be
equal to the measure of angle 𝐴𝐷𝐶. And that’s 37. So, using the property of inscribed
angles subtended from the same arc, we find the measure of angle 𝐵𝐶𝐷 is equal to
36 degrees and the measure of angle 𝐶𝐷𝐴 is equal to 37 degrees.
