In the given figure, two straight lines PQ and RS intersect each other at O. If ∠POT = 75°, find the values of a + b + c.

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In the given figure, two straight lines PQ and RS intersect each other at O. If ∠POT = 75°, find the values of a + b + c.
Lines and Angles Class 9 Extra Questions Maths Chapter 6 with Solutions Answers 10

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105^o

165^o

153^o

180^o

answer is C.

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Detailed Solution

Here, 4b + 75° + b = 180° [A straight angle]
5b = 180° – 75° = 105°
b = $\frac{105^{o}}{5}$ = 21°
∴ a = 4b = 4 × 21° = 84° [Vertically opposite angles]
Again, 2c + a = 180° [A linear pair]
⇒ 2c + 84° = 180°
⇒ 2c = 96°
⇒ c = $\frac{96^{o}}{2}$ = 48°
Hence, the values of a, b and c are: