Suppose 𝑀𝐸 bisects angle
𝐴𝑀𝐷. Find the measure of angle
So we are told that 𝑀𝐸 bisects
angle 𝐴𝑀𝐷, so it cuts it in half, and we wanna know the measure of angle
𝐸𝑀𝐶. So we’re given the 45 degrees, the
measure of angle 𝐶𝑀𝐵. And if it’s 45 degrees, angle
𝐴𝑀𝐷 is 45 degrees. This is because they are vertical
angles, and vertical angles are congruent.
So if 𝑀𝐸 bisected that 45-degree
angle, it cut 45 degrees in half. So angle 𝐴𝑀𝐸 would be 22.5
degrees and angle 𝐸𝑀𝐷 would be 22.5 degrees. So this is helpful because now we
know this portion of the angle that we’re looking for; 𝐸𝑀C is 22.5 degrees.
So now we need to find this
remaining portion. Well, if 𝐵𝐷 is a straight line,
then it should add to 180 degrees, and we already know this much of it is 45
degrees, so the remaining will be the piece that we need.
So 180 minus 45 would give us 135
degrees, so the angle that we’re looking for, 𝐸𝑀𝐶, will be 135 degrees plus 22.5
degrees. And adding these together, we would
get 157.5 degrees, so that would be the measure of angle 𝐸𝑀𝐶.