#### Question

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

#### Solution

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°

Is there an error in this question or solution?

Solution In the Given Figure, ∠Ace = 43° and ∠Caf = 62° ; Find the Values of A, B and C. Concept: Arc and Chord Properties - Angles in the Same Segment of a Circle Are Equal (Without Proof).