Plz help im stumped and this is due today plz help!

Question

m∠XYZ = 117° Find m∠XYW and m∠WYZ.

m∠XYW = ___ °

m∠WYZ = ____°

Answer 1

Note that angle XYZ is a sum of angles XYW and WYZ, in other words m(XYZ)=m(XYW)+m(WYZ)

But:

m(XYZ)=117

m(XYW)=6x+44

m(WYZ)=-10x+65

or:

117=6x+44+(-10x+65)

We now solve last equation to find x:

117=6x+44-10x+65

117=-4x+109

117-109=-4x+109-109

8=-4x

x=-2

Using x=-2 we calculate:

m(XYW)=6x+44=6(-2)+44=-12+44=32

m(WYZ)=-10x+65=-10(-2)+65=20+65=85

If you check the answer we get: 117=32+85

Answer 2

By angle addition, m<XYW + m<WYZ = m<XYZ

So

6x + 44 + -10x + 65 = 117

-4x + 109 = 117

-4x = 8

x = -2

so m<WYZ = -10x + 65 = -10(-2) + 65 = 85