Question : The sum of the angles made by a chord at the centre and on the major arc of a circle is 180 degrees. What will be the angle made at the centre of the circle?
Option 1: 60 degrees
Option 2: 90 degrees
Option 3: 75 degrees
Option 4: 120 degrees
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Correct Answer: 120 degrees
Solution : The angle at the center is twice the angle at the major arc. Let the angle made at the centre be $2xº$ Angle made at major arc = $x°$ $⇒ 2xº + xº = 180º$ $⇒ 3xº = 180º$ $⇒ xº = 60º$ $⇒ 2xº = 120º$ Therefore, the angle made at the centre of the circle is 120º. Hence, the correct answer is 120 degrees.
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