Q1 of 32 Page 67

In Figure 5.59 if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60° then QRS is equal to-

Now after observing the figure:

It is given PQ || RS which implies that,


∠ PQC = ∠ BRS = 60° [Alternate exterior angles and ∠ PQC = 60°]


∠ DQA = ∠ QRA = 25° [Alternate interior angles and ∠ DQR = 25°]


∠ QRS = ∠ QRA + ∠ ARS


= ∠ QRA + [180° - ∠ BRS]


= 25° + [180° - 60°]


= 25° + 120°


= 145°


Alternate Exterior Angles:


If two lines are parallel and is cut by transversal, then alternate exterior angles are equal.



In the above figure, L || M so ∠ 1 = ∠ 2


Alternate Interior Angles:


If two lines are parallel and is cut by transversal, then alternate interior angles are equal.



In the above figure, L || M so ∠ 1 = ∠ 2


So the correct answer is C.

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