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Write the correct answer in each of the following:
$\text{In Fig. 6.1, if }AB \parallel CD \parallel EF, PQ \parallel RS,$ $\angle RQD = 25^{\circ}$ $\text{ and }\angle CQP = 60^{\circ}$ $\text{ and }\angle CQP = 60^{\circ} \text{, then}$ $\angle QRS \text{ is equal to }$

$(A)\ 85^{\circ}$

$(B)\ 135^{\circ}$

$(C)\ 145^{\circ}$

$(D)\ 110^{\circ}$

Answers (1)

Solution.

Here in this question, it is given,
$PQ \parallel RS$
$\angle PQC = \angle BRQ = 60^{\circ}$ $\text{(Alternate Exterior angles)}$
$\angle PQC = 60^{\circ}$
$\angle DQR = \angle QRA= 25^{\circ}$ $\text{(Alternate interior angles)}$
$\angle QRS = \angle QRA + \angle ARS$
$= \angle QRA + (180^{\circ} - \angle BRS)$ $\text{(Linear pair angle)}$
$= 25^{\circ} + 180^{\circ} - 60^{\circ} = 205^{\circ} - 60^{\circ} = 145^{\circ}$

Hence, option C is the right answer.

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infoexpert26

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