Mathematics
Grade9
Easy

Question

Find the value of angle ABC if AB = BC.

  1. 80°
  2. 100°
  3. 120°
  4. 20°

hintHint:

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°.

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