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Question
In the following figure, PQ || RS. If ∠1 = (2a + b)° and ∠6 = (3a – b)°, then the measure of ∠2 in terms of b is ______.
Options
(2 + b)°
(3 – b)°
(108 – b)°
(180 – b)°
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Solution
In the following figure, PQ || RS. If ∠1 = (2a + b)° and ∠6 = (3a – b)°, then the measure of ∠2 in terms of b is (108 – b)°.
Explanation:
Since, PQ || RS and line 1 is a transversal.
∴ ∠2 = ∠6 = (3a – b)° ...(i) [Corresponding angles]
∠1 + ∠2 = 180° ...[Angles on a straight line PQ]
⇒ ∠2 = 180° – (2a + b)° ...(ii) [∵ ∠1 = (2a + b)° (given)]
From (i) and (ii), we have
⇒ (3a – b)° = 180° – (2a + b)°
⇒ 3a – b = 180° – 2a – b
⇒ 3a – b + 2a + b = 180°
⇒ 5a = 180°
⇒ a = `180^circ/5` = 36°
∴ a = 36°
Now, ∠2 – (3a – b)° ...[From (i)]
⇒ ∠2 = (3 × 36° – b)° = (108 – b)°
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