Multiple choice

Choose the correct answer from the alternatives given. AB is a diameter of a circle with centre at O. DC is a chord of it such that DC || AB. If $\angle BAC \, = \, 20^\circ$, then $\angle ADC$ is equal to

  1. 120$^\circ$
  2. 110$^\circ$
  3. 115$^\circ$
  4. 100$^\circ$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since DC || AB, angle BAC = angle ACD = 20 degrees (alternate interior angles). In circle, OA = OC (radii), so triangle OAC is isosceles. Angle OAC = angle OCA = 20 degrees. Angle AOC = 180 - 20 - 20 = 140 degrees. Angle ADC = 1/2 * (360 - 140) = 110 degrees (angle at circumference is half the reflex angle at center).

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