ABCD is cyclic quadrilateral such that AB is a distance of the circle circum scribing it and ∠ADC = 148°. What is the measure of the ∠BAC ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 58°
Here ABCD is the cylic quadrilateral.
∠ADC = 148°
Angle subtended by a diameter/semicircle on any point of circle is 90° right angle.
∠ACB = 90°
In cylic quadrilateral, the sum of the opposite angle is 180°.
⇒ ∠ADC + ∠ABC = 180°
⇒ 148° + ∠ABC = 180°
⇒ ∠ABC = 32°
In triangle ABC :
∠ABC + ∠ACB + ∠BAC = 180°
⇒ 32° + 90° + ∠BAC = 180°
⇒ ∠BAC = 180° - 122°
⇒ ∠BAC = 58°