Answer:
a) UXW = 78 b) UWY = 48 c) WZX = 48 d) XYZ = 42
Step-by-step explanation:
There are many ways you can do this, but I'll just describe one for each.
a) Angle YWV is vertical to XWZ, so they are congruent. Angle XWZ is an alternate interior angle with angle UXW, so UXW = 78.
b) All the angles that revolve around point W must add up to 360. We already know 4 angles due to vertical angles, so 78 + 78 + 54 + 54 = 264.
360 - 264 = 96. There are two angles left, and since they are vertical they must be congruent. 96/2 = 48, so angle UWY is 48 degrees.
c) We already know that the angle vertical to UWY is 48, so WZX is also 48 degrees because they are alternate interior angles.
d) Angle UWY is 48 degrees and angle WUY is 90 degrees because of the perpendicular line. Now we can find XYZ, the remaining angle.
90 + 48 = 138. 180 - 138 = 42. So XYZ = 42 degrees.
I hope this helped. I'm open to any questions you may have. :)
