1.

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°

Answer»

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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