Question

In the diagram, the value of a+b -

Answer 1

Answer :-

→ ∠FEB + ∠BED = 180° { Linear pair. }

→ 130° + ∠BED = 180°

→ ∠BED = 180° - 130° = 50° ------- Eqn.(1)

now, in ∆ACB,

→ ∠CBD = ∠BAC + ∠ACB { Exterior angle is equal to sum of opposite interior angles. }

→ ∠CBD = (50° + b) ------- Eqn.(2)

now, in ∆EBD,

→ ∠EBD + ∠BED + ∠EDB = 180° { Angle sum Property.}

putting values from Eqn.(1) and Eqn.(2)

→ (50° + b) + 50° + a = 180°

→ 100° + a + b = 180°

→ (a + b) = 180° - 100°

→ (a + b) = 80° (Ans.)

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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