Question

C is a point on the minor arc AB of the circle with centre O. Given ∠ACB = x. Calculate ∠x , if ACBO is a parallelogram.



• A. $x={120}^{\circ }$
• B. $x={90}^{\circ }$
• C. $x={10}^{\circ }$
• D. $x={87}^{\circ }$

Answer 1

Answer: (A)

$x={120}^{\circ }$

Clearly, major arc BA subtends $\angle x$ at a point on the remaining part of the circle.
$\therefore$ Reflex $\angle AOB=2x$


$\Rightarrow {360}^{\circ }-y=2x$
$\Rightarrow y={360}^{\circ }-2x$
Thus, $y={360}^{\circ }-2x$
Since ACBO is a parallelogram.
$\therefore x=y\Rightarrow x={360}^{\circ }-2x$
$\Rightarrow 3x={360}^{\circ }\Rightarrow x={120}^{\circ }$