Question 41

In the given figure, if PQ|| RS and QR || TS, then the value of a is

(a) $95^{\circ}$
(b) $90^{\circ}$
(c) $85^{\circ}$
(d) $75^{\circ}$

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Solution

Since, PQ ||RS and QR is transversal.
$∴ ∠ PQR = ∠ S R Q \Rightarrow ∠ SRQ = 85^{\circ}$
Also, ST || QR and RS is transversal.
$∴ ∠ SRQ = ∠ RST$
Now $∠ {RST + a = 180}^{\circ} \Rightarrow ∠ {RST + a = 180}^{\circ} \Rightarrow {a = 180}^{\circ} - 85^{\circ} \Rightarrow {a = 95}^{\circ}$

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Similar questions

In the given figure AB||CD.
If $∠ C D E = 85^{\circ}$ ,then find the value of x and y respectively.

In the given figure, $O$ is the centre of a circle. If $∠ A O B = 100^{\circ}$ and $∠ A O C = 90^{\circ}$ , then $∠ B A C = ?$

(a) $85^{\circ}$

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(d) $75^{\circ}$

Question 8

In the given figure, PB = PD. The value of x is

a) $85^{\circ}$
b) $90^{\circ}$
c) $25^{\circ}$
d) $35^{\circ}$

75^{\circ}, 90^{\circ} a n d 75^{\circ}

90^{\circ}

95^{\circ}

105^{\circ}

120^{\circ}

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