Question

In the given figure, ∠ACE = 43° and ∠CAF = 62°; find the values of a, b and c.

Answer 1

Now, ∠ACE = 43° and ∠CAF = 62°  ...[Given]

In ΔAEC

∴ ∠ACE + ∠CAE + ∠AEC = 180°

`=>` 43° + 62° + ∠AEC = 180°

`=>` 105° + ∠AEC = 180°

`=>` ∠AEC = 180° – 105° = 75°

Now, ∠ABD + ∠AED = 180°  ...[Opposite angles of a cyclic quad and ∠AED = ∠AEC]

`=>` a + 75° = 180°

`=>` a = 180° – 75°

`=>` a = 105°

∠EDF = ∠BAF

∴ c = 62°   ...[Angles in the alternate segments]

In ΔBAF, a + 62° + b = 180°

`=>` 105° + 62° + b = 180°

`=>` 167° + b = 180°

`=>` b = 180° – 167° = 13°

Hence, a = 105°, b = 13° and c = 62°.