Answer
Angle XYW = 32°
Angle WYZ = 85°
Step-by-step explanation
We've been told that
Angle XYZ = 117°
We've also been given that
Angle XYW = (6x + 44)°
Angle WYZ = (-10x + 65)°
But, from the figure in the attached image, we can see that
Angle XYW + Angle WYZ = Angle XYZ
(6x + 44)° + (-10x + 65)° = 117°
6x - 10x + 44° + 65° = 117°
-4x + 109° = 117°
-4x = 117° - 109°
-4x = 8°
Divide both sides by -4
(-4x/-4) = (8°/-4)
x = -2°
We can then go further and solve for the required angles now
Angle XYW = (6x + 44)°
= 6(-2°) + 44°
= -12° + 44°
= 32°
Angle WYZ = (-10x + 65)°
= -10(-2°) + 65°
= 20° + 65°
= 85°
Hope this Helps!!!