Triangle UVW is shown with m∠WUV = 36°. The measure of ∠UVW is (5h − 68)°, and the measure of ∠AWB is (5h − 20)°.
triangle UVW with side VW extended through point A and side UW extended through point B, with angle U labeled as 36 degrees
Determine the value of h.
a) h = 48
b) h = 24.5
c) h = 23.2
d) h = 21
Since ∠WUV is given as 36° and UVW is labeled as (5h - 68)°, we can set up an equation to find the value of h.
∠WUV + ∠UVW + ∠U = 180° (sum of angles in a triangle)
36° + (5h - 68)° + ∠U = 180°
Combine like terms:
5h - 32 + ∠U = 180°
Now, the measure of ∠AWB is labeled as (5h - 20)°, and since ∠UVW is part of triangle UVW, we can use the Exterior Angle Theorem to relate the two angles.
∠AWB = ∠U + ∠UVW
(5h - 20)° = ∠U + (5h - 68)°
Combine like terms:
5h - 20 = ∠U + 5h - 68
Subtract 5h from both sides:
-20 = ∠U - 68
Add 68 to both sides:
48 = ∠U
Now we can substitute this value back into our first equation:
36 + (5h - 68) + 48 = 180
Combine like terms:
5h + 16 = 180
Subtract 16 from both sides:
5h = 164
Divide both sides by 5:
h = 32.8
None of the given answer choices match this value of h. Therefore, there may be an error in the problem or the solution approach.