Answer: We know that T is the midpoint of VW, which means that ZW = ZV. So we can say that ZV = ZW = 41°.
Also, we know that Y is the midpoint of UW, so the angle ZYU is half of ZUW. So we can say that ZYU = ZUW/2.
We know that X is the midpoint of UV, so the angle ZXU is half of ZUV. So we can say that ZXU = ZUV/2.
Since Y is the midpoint of UW, ZYU + ZXU = ZUW/2 + ZUV/2 = ZUW/2 + (ZUW - ZXU)/2 = ZUW/2 + (ZUW - ZUV/2)/2 = ZUW/2 + (ZUW - ZUW/2)/2 = ZUW/2 + ZUW/4 = (3/4)ZUW
We know that X is the midpoint of UV, so ZXU + ZVU = ZUV/2 + ZUV = ZUV
The angle ZTYW is supplementary to the angle ZXU + ZVU + ZYU so mZTYW = 180 - ( ZXU + ZVU + ZYU)
Therefore, mZTYW = 180 - ( ZUV + (3/4)ZUW + 41)
mZTYW = 180 - (56 + (3/4)56 + 41) = 180 - (56 + 42 + 41) = 180 - 139 = 41 degrees
Explanation: