Question

Given a circle with the center indicated, find $x.$

• A. ${100}^{\circ }$
• B. ${80}^{\circ }$
• C. ${50}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is D ${40}^{\circ }$

We know that the angle at the centre is twice is the angle at the circumference subtended by the same arc.

Here angle at the circumference is $x$

Let the triangle be $ABC$.

Thus the angle at the center $B$ is $2x$.

Since $AB$ and $BC$ are the radius of the circle, they are of the same length.

So, $\angle A=\angle C={50}^{\circ }$

Now,

$2x+{50}^{\circ }+{50}^{\circ }={180}^{\circ }$
$\Rightarrow 2x={180}^{\circ }-{100}^{\circ }$

$\Rightarrow 2x={80}^{\circ }$

$\Rightarrow x={40}^{\circ }$