In Fig. 6.31, if PQ || ST, ∠ PQR = 110° and ∠ RST = 130°, find ∠ QRS. [Hint: Draw a line parallel to ST through point R.]

Question

In Fig. 6.31, if PQ || ST, &#x2220; PQR = 110&#xB0; and &#x2220; RST = 130&#xB0;, find &#x2220; QRS. [Hint: Draw a line parallel to ST through point R.]

Philoid · Accepted Answer

It is given in the question that:

PQ parallel ST,

∠PQR = 110^o and,

∠RST = 130^o

Construction: Draw a line XY parallel to PQ and ST

∠PQR + ∠QRX = 180^o (Angles on the same side of transversal)

110^o + ∠QRX = 180^o

∠QRX = 70^o

And,

∠RST + ∠SRY = 180^o (Angles on the same side of transversal)

130^o + ∠SRY = 180^o

∠SRY = 50^o

Now,

∠QRX + ∠SRY + ∠QRS = 180^o

70^o + 50^o + ∠QRS = 180^o

∠QRS = 60^o

In Fig. 6.31, if PQ || ST, ∠ PQR = 110° and∠ RST = 130°, find ∠ QRS.[Hint: Draw a line parallel to ST through point R.]

In Fig. 6.31, if PQ || ST, ∠ PQR = 110° and∠ RST = 130°, find ∠ QRS.
[Hint: Draw a line parallel to ST through point R.]