Question
Download Solution PDFIn a circle, ABCD is a cyclic quadrilateral. AC and BD intersect each other at P. If AB = AC and ∠BAC = 48°, then the measure of ∠ADC is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
AB = AC and ∠BAC = 48°
Concept used:
The sum of the opposite angles of a cyclic quadrilateral = 180°
Calculation:
∠ABC = ∠ACB [∵ AB = AC]
∠BAC + ∠ABC + ∠ACB = 180°
So, ∠ABC = ∠ACB = (180° - 48°)/2 = 132°/2 = 66°
Also, ∠ADC + ∠ABC = 180°
⇒ ∠ADC + 66° = 180°
⇒ ∠ADC = 180° - 66° = 114°
∴ The measure of ∠ADC is 114°
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