Question

in the diagram, roads a and b are parallel. solve for x and find the measure of ∠wuv.
(9x)°
(22x + 25)°
x=

m∠wuv=

Explanation:

Step1: Identify angle - relationship

Since roads a and b are parallel, the angles (9x)° and (22x + 25)° are corresponding angles and are equal. So, 9x=22x + 25.

Step2: Solve the equation for x

Subtract 9x from both sides: 0 = 22x-9x + 25, which simplifies to 0 = 13x+25. Then subtract 25 from both sides: - 25 = 13x. Divide both sides by 13: x=-\frac{25}{13}. But this is incorrect. The correct relationship is that (9x)° and (22x + 25)° are same - side exterior angles and they are supplementary. So, 9x+(22x + 25)=180.

Step3: Simplify the equation

Combine like - terms: (9x+22x)+25 = 180, which gives 31x+25 = 180.

Step4: Solve for x

Subtract 25 from both sides: 31x=180 - 25=155. Divide both sides by 31: x = 5.

Step5: Find the measure of ∠WUV

Substitute x = 5 into the expression for ∠WUV which is (22x + 25)°. So, m∠WUV=22×5+25=110 + 25=135°.

Answer:

x = 5
m∠WUV = 135°