Question

For this item, any answers that are not whole numbers should be entered as a decimal, rounded to the tenths place. In the figure below, line AB, line CD, and line EF intersect at point Q. Line AB is perpendicular to line CD. Complete the following equations.

x =
m∠CQF =
m∠AQE =

Answer 1

x = 10

m∠CQF = 32

m∠AQE = 58

Explanation:

Answer 2

`x = 10`

m<CQF = 32°

m<AQE = 32°

Explanation:

m<CQB = m<CQA = 90° (right angle)

m<CQB = m<CQF + m<FQB

m<CQF = 3x + 2

m<FQB = 58°

Therefore,

`90 = 3x + 2 + 58`

Solve for x:

`90 = 3x + 60`

`90 - 60 = 3x + 60 - 60`

`30 = 3x`

`(30)/(3) = (3x)/(3)`

`10 = x`

`x = 10`

m<CQF = 3x + 2

Plug in the value of x to find m<CQF

m<CQF = 3(10) + 2 = 30 + 2

m<CQF = 32°

m<CQF and m<AQE are vertical opposite angles, therefore, they are congruent.

Thus,

m<AQE = 32°