Triangle UVW is shown with m∠WUV = 36°. The measure of ∠UVW is (5h − 66)°, and the measure of ∠AWB is (5h − 18)°.
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.
h = 22.8
h = 23
h = 25.4
h = 48
To find the value of h, we need to use the fact that the sum of the angles in a triangle is 180 degrees.
We know that m∠WUV = 36° and m∠UVW = (5h - 66)°.
Since we also have a line extension of VW passing through point A, we can use the fact that the sum of the angles on a straight line is 180 degrees.
Therefore, m∠AWB = 180 - m∠UVW.
Substituting m∠UVW = (5h - 66)°, we have m∠AWB = 180 - (5h - 66)° = (5h - 114)°.
Now we can use the fact that the sum of the angles in a triangle is 180 degrees.
m∠WUV + m∠UVW + m∠AWB = 180
36 + (5h - 66) + (5h - 114) = 180
10h - 144 = 180
10h = 324
h = 32.4
Therefore, none of the given options is the correct value of h.