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PBA and PDC are two secants. AD is the diameter of the circle with center at O. ∠A = 40°, ∠P = 20°. Find the measure of ∠DBC.

(a) 30° 

(b) 45° 

(c) 50° 

(d) 40°

1 Answer

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Answer : (a) 30º 

In ∆ ADP, ext. ∠ADC = Int. ∠s (∠A + ∠P) 

= 40° + 20° = 60°. 

∠ABC = ∠ADC = 60° (Angles in the same segment)

\(\because\) AD is the diameter, ∠ABD = 90°

∴  ∠DBC = ∠ABD – ∠ABC = 90° – 60° 

= 30°

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