In the given figure- P Q ST - T V RS and T U - ST- Find - QRS-A- None of theseB- 120- 125-D- 135-

The correct option is D 135^∘Join RX ∠ RXS = ∠ PQR = 70^∘ (Alternative angles) Also, ∠ STV = ∠ RSX (Alternative angles) But ∠ STV = 90^∘ 25^∘ = 65^∘ ∴∠ RSX ...

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Quantitative Aptitude

Lines and Angles

In the given ...

Question

In the given figure, $P Q | | S T, T V | | R S a n d T U ⊥ S T .$ Find $∠ Q R S .$

120^{\circ}

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125^{\circ}

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135^{\circ}

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None of these

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Solution

The correct option is C $135^{\circ}$
Join RX
$∠ R X S = ∠ P Q R = 70^{\circ}$ (Alternative angles)
Also, $∠ S T V = ∠ R S X$ (Alternative angles)

But $∠ S T V = 90^{\circ} - 25^{\circ} = 65^{\circ} ∴ ∠ R S X = 65^{\circ} ∠ Q R S = ∠ R S X + ∠ R X S = 70^{\circ} + 65^{\circ} = 135^{\circ}$

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In the given figure, PQ||ST,TV||RS and TU ⊥ ST. Find ∠QRS.

The correct option is C 135∘Join RX ∠RXS=∠PQR=70∘ (Alternative angles) Also, ∠STV=∠RSX (Alternative angles) But ∠STV=90∘−25∘=65∘∴∠RSX=65∘∠QRS=∠RSX+∠RXS=70∘+65∘=135∘

In the given figure, $P Q | | S T, T V | | R S a n d T U ⊥ S T .$ Find $∠ Q R S .$