Question

PLEASE ANSWER BOTH PARTS!

In the figure shown, line AB is parallel to line CD.
Part A: What is the measure of angle x? Show your work.
Part B: Explain how you found the measure of angle x by identifying the angle relationships that you used along the transversal.

REFER TO GRAPH BELOW.

Answer 1

A)
`m\angle x=55\°`

B) Angle relationship used to find
`\angle x` was alternate interior angles of a traversal between two parallel lines

Explanation:

Given :

`AB\parallel CD`

`m\angle APQ=65\°`

`m\angle PRD=120\°`

To find measure of
`\angle x`.

Part A

From the figure we can say:

`m\angle PQR=m\angle APQ` [Alternate interior angles are congruent]

∴
`m\angle PQR=65\°` [By substitution ∵
`m\angle APQ=65\°`]

For Δ PQR

`m\angle PQR+m\angle x=120\°` [Sum of two interior angles of a triangle is equal to the opposite exterior angle]

`m\angle x=120\°-m\angle PQR` [By subtraction property of equality]

`m\angle x=120\°-65\°` [By substitution ∵
`\angle PQR=65\°`

`m\angle x=55\°`

Part B:

We used the angle relationship of alternate interior angles of traversal
`PQ` between two parallel lines
`AB\ and\ CD` to find measure one angle of the Δ PQR which in turn helped us to find the measure of other angle of triangle which is
`\angle x` as the two angles found are opposite to the exterior angle that is =120°

Relation used:

`m\angle PQR=m\angle APQ` [Alternate interior angles are congruent]

`m\angle PQR=65\°` [By substitution ∵
`m\angle APQ=65\°`]