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Question
In the following figure, find the values of a, b and c.
Diagram
Sum
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Solution
In figure,
In ΔPQS, ∠QPS = ∠PQS + ∠PSQ = 180° ...[Sum of all the angles of a triangle is 180°]
⇒ 55° + 60° + a = 180°
⇒ 115° + a = 180°
⇒ a = 180° – 115° = 65°
Now, a + b = 180° ...[Linear pair has sum of 180°]
⇒ 65° + b = 180°
⇒ b = 180° – 65° = 115°
In ΔPSR, ∠PSR = ∠SPR + ∠PRS = 180° ...[Sum of all the angles of a triangle is 180°]
⇒ 115° + c + 40° = 180°
⇒ 155° + c = 180°
⇒ c = 180° – 115° = 25°
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Chapter 6: Triangles - Exercise [Page 172]
