Question

In the given figure, ${}^{\prime }{O}^{\prime }$ is the centre of the circle and $\angle ABC=40^{\circ }$. Determine the measure of reflex $\angle AOC$

• A. $120^{\circ }$
• B. $270^{\circ }$
• C. $280^{\circ }$
• D. $330^{\circ }$

Answer 1

Answer: (C)

Given, $\angle ABC=40^{\circ }$.
An angle subtended by an arc at the centre of the circle is double the angle subtended
by the same arc at any point on the remaining part of the circle.
$\angle AOC=2\angle ABC=80^{\circ }$
$\therefore \text{ Reflex }\angle AOC$
$=360^{\circ }-80^{\circ }=280^{\circ }$