Question

Triangle UVW is shown with m∠WUV=36° . The measure of ∠UVW is 5h−64° , and the measure of ∠AWB is 5h−16∘.

a. h=10
b. h=12
c. h=14
d. h=16

Answer 1

To find the value of h, the given angle measures are added and set equal to 180° to use the triangle angle sum theorem. However, the calculation results in h = 22.4°, which does not match any of the provided options, indicating a possible error in the question or options.

Step-by-step explanation:

The question involves solving for the variable h in a triangle using given angle expressions. Triangle UVW has two angles expressed using the variable h: m∠UVW = 5h - 64° and m∠AWB = 5h - 16°. Given that the sum of angles in a triangle equals 180°, we set up an equation: 36° + (5h - 64°) + (5h - 16°) = 180°. Solving this equation will provide the value of h.

To solve for h, we combine like terms and subtract the constants from both sides of the equation:

1. Combine the terms: 36° - 64° - 16° + 10h = 180°.
2. Simplify: 10h - 44° = 180°.
3. Add 44° to both sides: 10h = 224°.
4. Divide by 10: h = 22.4°. Note: This value doesn't match any of the options given, which may suggest a typo or error in the given options or question.