Question

Find x and m of angle wyl

Answer 1

Explanation:

x is clearly 42° because WU is an angle bisector of YWZ (which is 84, and bisecting means half of 84, that is 42)

now, for m of WYL

notice, YLW = 90°

also, UWL = 42°

name the intersection point of YL and WU as O in your mind

Apply angle sum property of a triangle for triangle WOL

angle WOL + angle UWL + angle YLW = 180

angle WOL + 90 + 42 = 180

angle WOL = 180 - 132

angle WOL = 48

now focus on line LOY

since LOY is a line, the angles a line intersecting it forms a linear pair, i.e

angle WOL + angle YOW = 180

48 + YOW = 180

angle YOW = 132

Now, apply angle sum property for triangle YOW

angle YOW + angle YWO (x) + angle WYO (or WYL) = 180

132 + 42 + WYO (or WYL) = 180

WYO (or WYL) = 6°

ask me in the comments if you have any doubts in this