Question

1. In the figure, AB || CD and PQ is the transversal, angle PQM = x and angle QPA = 120 + x then
(i). What is the measure of angle PQC.
(ii). Apply interior angles theorem and frame an equation.
(iii). Find x ​

Answer 1

Answer:

(i) m(<PQC) = 30

(iii) x = 30

Answer 2

Given:

AB || CD and PQ is the transversal.

∠DQM = $x$

∠QPA = $120+x$

To find:

Measure of ∠PQC.

The value of $x$.

Solution:

When AB || CD and PQ is the transversal, then by alternate interior angle theorem,

∠QPA = ∠DQP = $120+x$

Now, ∠DQP and ∠DQM lie on the same line PQ. Hence, their sum is supplementary.

∠DQP + ∠DQM = 180

$120+x+x=180$

$2x=180-120$

$2x=60$

$x=\frac{60}{2}=30^{0}$

Now, ∠QPA and ∠BPQ are on the same line AB. Their sum is also supplementary.

Let ∠BPQ = $y$

∠QPA + ∠BPQ = 180

$120+x+y=180$

$120+30+y=180$

$y=180-120-30=30$

Now, ∠BPQ = ∠PQC because they are alternate interior angles. Hence,

∠PQC = 30°

Measure of ∠PQC = 30°.

Measure of $x=30^{0}$.