Question

PLEASE ANSWER BOTH PARTS!

Answer 1

Answer:

A) $m\angle x=55\°$

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

Step-by-step 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 ∵ $m\angle APQ=65\°$]