Question

Find the values of a, b and c in the figure given below.
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Answer 1

Answer:

a = 180 - (60 + 55) = 65

60= b (Corresponding angles)

c= 180- (60+ 40)= 80

Answer 2

In the given figure,

• ∠QPR = 55° + c

By Angle Sum Property,

∠PQR + ∠PRQ + ∠QPR = 180°

⇒ 60° + 40° + (55° + c) = 180°

⇒ 100° + 55° + c = 180°

⇒ 155 + c = 180°

⇒ c = 180° - 155

∴ c = 25°

Now in ΔPSR,

By Exterior Angle Property,

∠PSR = ∠QPS + ∠PQS

⇒ b = 55° + 60°

∴ b = 115°

We know the value of b

Applying Linear Pair of angles;

∠PSR + ∠PSQ = 180°

⇒ 115° + a = 180°

⇒ a = 180° - 115°

∴ a = 65°

Know more:

• Angle sum property states that sum of all angles in a triangle is 180°

• Exterior Angle Property states that Exterior angle is equal to sum of opposite 2 interior angles.

• Linear Pair of angles states that sum of 2 or more angles lying on a straight line is always 180°