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