In a circle with center O, an arc ABC subtends an angle of 138° at the centre of the circle. The chord AB is produced to a point P. Then, the measure of is:
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 69°.
Here, ∠AOC = 138°
So, Reflex∠AOC = 360° - 138° = 222°
The angle subtended by an arc at the center of a circle is twice the angle subtended at any point on the remaining part of the circumference.
∠ABC = (1/2) × 222° = 111°
Since AB is produced to P, angles ∠ABC and ∠CBP form a linear pair. This means their sum is 180°:
So, ∠ABC + ∠CBP = 180°
⇒ 111° + ∠CBP = 180°
⇒ ∠CBP = 180° - 111° = 69°
Therefore, the measure of ∠CBP is 69°.