Question

In the given figure, if ∠BAC = 60° and ∠BCA = 20°, find ∠ADC. 

Answer 1

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°`