Minor arc BC subtends angle BAC and BDC at points A and D. respectively, on the circumference in the major sector of the circle with center O. What is the value (in degrees) of (∠ABC + ∠ACB) if ∠BDC = 73°
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 107°.
∠ADC = 73°
∠ADC = ∠BAC = 73° (Angle from the same chord on the circumference are same)
In triangle ABC
∠BAC + ∠ABC + ∠ACB = 180°
⇒ 73° + x + y = 180°
⇒ x + y = 180° - 73°
⇒ x + y = 107°
So, the value of ∠ABC + ∠ACB = 107°