Question

4. In Fig. 6.31, if PQ || ST, Z PQR = 110° and
ZRST=130°, find 2 QRS.
[Hint : Draw a line parallel to ST through
point R.)​

Answer 1

Answer:

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Answer 2

Correct Question :-

If PQ || ST , ∠PQR = 110° and ∠ RST = 130° find ∠QRS .

$\bf{\underline{Given}}:-$

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

To find :-

• ∠ QRS = ?

Solution :-

∠PQR + ∠QRX = 180° (co interior angles)

110° + ∠QRX = 180°

∠QRX = 180° - 110°

∠QRX = 70°

Then,

∠RST + ∠SRY = 180° (co interior angles)

130° + ∠SRY = 180°

∠SRY = 180° - 130°

∠SRY = 50°

Now,

XY is a straight line.

QR and SR stand on it.

so,

∠QRX + ∠SRY + ∠QRS = 180°

70° + 50° + ∠QRS = 180°

120° + ∠QRS = 180°

∠QRS = 180° - 120°

∠QRS = 60°

Hence,∠QRS will be 60°.