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In the figure, if PQ ST, PQR={ 110 }^{ } and RST={ 130 }^{ },

Question

In the figure, if $PQ ∥ ST, ∠ PQR = 110$ and $∠ RST = 130$ , find $∠ QRS$ .

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In the figure, if

PQ ∥ ST, ∠ PQR = 110

and

∠ RST = 130

, find

∠ QRS

5 mins ago

Discuss this question LIVE

5 mins ago

Text solutionVerified

PQ ∥ ST, ∠ PQR = 11 0^{\circ}

and

∠ RST = 13 0^{\circ}

Construction: A line

X Y

parallel to

PQ

and

ST

is drawn.

∠ PQR + ∠ QRX = 18 0^{\circ}

(Angles on the same side of transversal.)

\Rightarrow 11 0^{\circ} + ∠ QRX = 18 0^{\circ}

\Rightarrow ∠ QRX = 7 0^{\circ}

Also

∠ RST + ∠ SR Y = 18 0^{\circ}

(Angles on the same side of transversal.)

13 0^{\circ} ° + ∠ SR Y = 18 0^{\circ}

∠ SR Y = 5 0^{\circ}

Now,

∠ QRX + ∠ SR Y + ∠ QRS = 18 0^{o}

\Rightarrow 7 0^{\circ} + 5 0^{\circ} + ∠ QRS = 18 0^{\circ}

∴ ∠ QRS = 6 0^{\circ}

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Question Text	In the figure, if $PQ ∥ ST, ∠ PQR = 110$ and $∠ RST = 130$ , find $∠ QRS$ .
Answer Type	Text solution:1
Upvotes	150