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प्रश्न
In the following figure, if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then ∠QRS is equal to ______.
विकल्प
85°
135°
145°
110°
उत्तर
In the following figure, if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then ∠QRS is equal to 145°.
Explanation:
Given, PQ || RS
∠PQC = ∠BRS = 60° ...[Alternate exterior angles and ∠PQC = 60° (given)]
And ∠DQR = ∠QRA = 25° ...[Alternate interior angles]
∠DQR = 25° ...[Given]
∠QRS = ∠QRA + ∠ARS
= ∠QRA + (180° – ∠BRS) ...[Linear pair axiom]
= 25° + 180° – 60°
= 205° – 60°
= 145°
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