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.

113° 123° 102° 114°

113°

Since AB = AC, ∴ ∠ABC = ∠ACB = \(\frac{180°\;-\;46°}{2}\) = 180° - 46° = 67° Now, ∠ADC + ∠ABC = 180°                       (cyclic quadrilateral ) ∠ADC = 180° - ∠ABC = 180° - 67° = 113°