Question
Find the value of angle ABC if AB = BC.
- 80°
- 100°
- 120°
- 20°
Hint:
From Figure, ∠BAC + ∠CAD = 180°
The correct answer is: 20°
From Figure, ∠BAC + ∠CAD = 180° (Linear Pair)
⇒ ∠BAC + 100° = 180°
⇒ ∠BAC = 80°
In Δ ABC, ∠BAC = 80° (from above equation)
And AB = BC (Given)
⇒ ∠A = ∠C (Angles opposite to two equal sides of triangle are equal)
∠BAC + ∠ABC + ∠ACB = 180° (Angle Sum property of triangle)
⇒ 80° + ∠B + 80° = 180°
⇒ ∠B = 180° – 160°
⇒ ∠B = 20°.
⇒ ∠BAC + 100° = 180°
⇒ ∠BAC = 80°
In Δ ABC, ∠BAC = 80° (from above equation)
And AB = BC (Given)
⇒ ∠A = ∠C (Angles opposite to two equal sides of triangle are equal)
∠BAC + ∠ABC + ∠ACB = 180° (Angle Sum property of triangle)
⇒ 80° + ∠B + 80° = 180°
⇒ ∠B = 180° – 160°
⇒ ∠B = 20°.
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