In Fig. 16.184, if ∠BAC=60° and ∠BCA=20°, find ∠ADC.
Answers
Given : ∠BAC = 60° and ∠BCA = 20°.
To Find : ∠ADC
Proof :
In ∆ ABC,
Since Sum of the angles of a triangle is 180° :
∠BAC + ∠ABC + ∠BCA = 180°
60° + ∠ABC + 20° = 180°
80° + ∠ABC = 180°
∠ABC = 180° - 80°
∠ABC = 100°
Since, ABCD is a cyclic quadrilateral, and Sum of Opposite pair of angles in a cyclic quadrilateral is 180° :
∴ ∠ABC + ∠ADC = 180°
100° + ∠ADC = 180°
∠ADC = 180° – 100°
∠ADC = 100°
Hence, ∠ADC is 100°.
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Answer:
Step-by-step explanation:In ∆ ABC,
Since Sum of the angles of a triangle is 180° :
∠BAC + ∠ABC + ∠BCA = 180°
60° + ∠ABC + 20° = 180°
80° + ∠ABC = 180°
∠ABC = 180° - 80°
∠ABC = 100°
Since, ABCD is a cyclic quadrilateral, and Sum of Opposite pair of angles in a cyclic quadrilateral is 180° :
∴ ∠ABC + ∠ADC = 180°
100° + ∠ADC = 180°
∠ADC = 180° – 100°
∠ADC = 100°