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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