In a circle, ABCD is a cyclic quadrilateral. AC and BD intersect each other at P. If AB = AC and ∠BAC = 46°, then the measure of ∠ADC is.
Answer & explanation
Correct answer: option 1
Since AB = AC,
∴ ∠ABC = ∠ACB = \(\frac{180°\;-\;46°}{2}\) = 90° - 23° = 67°
Now,
∠ADC + ∠ABC = 180° (cyclic quadrilateral )
∠ADC = 180° - ∠ABC = 180° - 67° = 113°