PBA and PDC are two secants. AD is the diameter of the circle with the centre at O. ∠A = 30°, ∠P = 20°. Find the measure of ∠DBC.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 40°.
∠A = 30°, ∠P = 20°
The angles subtended by the same arc at the circumference of a circle are equal.
So, ∠BCD = 30°
The angle subtended by the diameter of a circle is always 90°
AD is a diameter. So, ∠ABD = 90°
Also, ∠PBD = 90°
Now, ∠BDP = 180° - ∠PBD - ∠P = 180° - 90° - 20° = 70°
∠BDC = 180° - ∠BDP = 180° - 70° = 110°
∠DBC = 180° - ∠BDC - ∠BCD = 180° - 110° - 30° = 40°
Therefore, the value of ∠DBC is 40°.