Question

In the given figure, if ∠ ACE = 43° and ∠CAF = 62°. Find the value of a, b, and c.

Answer 1

ABCE is cyclic quadrilateral.
∴ ∠ ABD + ∠ AED = 180°
and ∠ EAB + ∠ BDE = 180°
Now in Δ ACE
∠ A + ∠ C + ∠ E = 180°
62° + 43° + ∠ E = 180°
∠ E = 180° - 105° = 75°

So,
∠ ABD + ∠ AED = 180°
∴ a + 75° = 180°
∴ a = 105°
∠ EDF = ∠ BAE       ....(Exterior angle of cyclic quadrilateral)
∴ 62° = c
∴ c = 62°

In Δ ABF,
∠ ABF + ∠BAF + ∠BFA = 180°
∴ 105° + 62° + b = 180°
∴ 167° + b = 180°
∴ b = 180° - 167°
∴ b = 13°

a = 105°, b = 13° and c = 62°