Question

:. In the Figure, if PQ || ST, PQR = 110° and RST = 130°, find QRS.
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Answer 1

Answer:

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Step-by-step explanation:

Interior angles on the same side of the transversal:The pair of interior angles on the same side of the transversal are called consecutive interior angles or allied angles or co interior angles.

If a transversal intersects two Parallel Lines then each pair of interior angles on the same side of the transversal is supplementary.

If a transversal intersects two lines such that a pair of alternate interior angles is equal then the two lines are parallel.

SOLUTION :

Given :PQ || ST, ∠PQR = 110° and ∠RST = 130°

Construction:A line XY parallel to PQ and ST is drawn.

∠PQR + ∠QRX = 180° (Angles on the same side of transversal.)

110° + ∠QRX = 180°

∠QRX = 180° - 110°

∠QRX = 70°

Also,∠RST + ∠SRY = 180° (Angles on the same side of transversal.)

130° + ∠SRY = 180°

∠SRY = 50°

Now,∠QRX +∠SRY + ∠QRS = 180°

70° + 50° + ∠QRS = 180°

∠QRS = 60°

Hence, ∠QRS = 60°

Answer 2

Given :-

PQ || ST

PQR = 110°

RST = 130°

To Find :-

QRS = ?

Solution :-

Construct a line XY parallel to PQ.

(Please refer to the attachment for your reference)

We know that,

The angles on the same side of transversal is equal to 180°

According to the question,

PQR + QRX = 180°

QRX = 180°- 110°

QRX = 70°

In the same way,

RST + SRY = 180°

SRY = 180°- 130°

SRY = 50°

The linear pairs on the line XY-

QRX + QRS + SRY = 180°

Substituting their values,

QRS = 180° – 70° – 50°

QRS = 60°

Therefore, QRS is 60°