Question

The figure above displays a circle with centre O. $\angle AOC=aand\angle ABC=b$. The relationship between a and b = _________

• A. $a+9b={360}^o$
• B. $a+2b={360}^o$
• C. $a+2b={120}^o$
• D. $a+2b={368}^o$

Answer 1

The correct option is B

$a+2b={360}^o$

$\angle AOC=aand\angle ABC=b$.

Reflex $\angle AOC={360}^o-a$

Arc AC subtends reflex $\angle AOC$ at the centre and $\angle ABC$ at the remaining part of the circle.

$\angle ABC=\frac{1}{2}\times \text{reflex angle}\angle AOC$

$b=\frac{1}{2}({360}^o-a)$

$2b={360}^o-a$

$a+2b={360}^o$