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Question
In the given figure, if ∠BAC = 60° and ∠BCA = 20°, find ∠ADC.
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Solution
It is given that, `angle BAC = 60°` and `angle BCA = 20°`
We have to find the `angle ADC `
In given Δ ABC we have
`angle ABC + angle BCA + angle BAC `= 180° \[ \left( \text{ Angle sum property } \right)\]
\[ \Rightarrow \angle ABC = 180° - \left( 60° + 20° \right) = 100° \]
In cyclic quadrilateral ABCD we have
`angle B + angleD = 180°` (Sum of pair of opposite angles of a cyclic quadilateral is 180º)
Then,
`angle D = 180° - 100° `
`angle D = 80° `
Hence `angle ADC = 80°`
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