Question

3. In Figure 3, if PQ || ST,
ZPQR = 110°, and
ZRST = 130°, find ZQRS.
[Hint: Produce PQ to
intersect SR at X.]
Fig. 3​

Answer 1

Answer:

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.

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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 = 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°

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Answer 2

Answer:

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