In a circle with center O, an arc ABC subtends an angle of 134° at the centre of the circle. The chord AB is produced to a point P. ∠CBP is equal to:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 67°.
The angle subtended by an arc at the center of a circle is double the size of the angle subtended by the same arc at the circle's circumference.
Take any point Q on the circumference and join AQ and QC.
∠AOC = 134°
∠AQC = 1/2 × ∠AOC = 1/2 × 134° = 67°
Now, ∠CBP = ∠AQC [Exterior angle of cyclic quadrilateral]
So, ∠CBP = 67°
Therefore, the value of ∠CBP is 67°.