All India Counselling
Question : In the given circle with diameter AB, find the value of x.
Option 1: 40°
Option 2: 20°
Option 3: 30°
Option 4: 50°
Correct Answer: 40°
Solution : $\angle ABD = \angle ACD = 50º$ [Angles in the same segment] In triangle ABD, by angle sum property we have The angle in a semicircle is a right angle. ⇒ x + 50° + 90° = 180° ⇒ x = 180° – 140° ⇒ x = 40° Hence, the correct answer is 40°.
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