Question

In the given figure, find the value of x.

$
  (a){\text{ 6}}{{\text{8}}^0} \\
  (b){\text{ 6}}{{\text{3}}^0} \\
  (c){\text{ 25}}{{\text{2}}^0} \\
  (d){\text{ none of these}} \\
$

Answer 1

Hint: In this a geometrical figure given in question we need to find the value of angle x. Use the concept that the angle subtended at the center of the circle by an arc is twice the angle subtended at the circumference by the same arc. This will help you approach the solution to find the answer.

Complete step-by-step answer:

As we know that the angle subtended at the center of the circle by an arc is twice the angle subtended at the circumference by the same arc.

Therefore from figure minor arc AB subtends the angle AOB at the center and angle ACB at the circumference.

Therefore from the above property we can say that,
\[ \Rightarrow \angle AOB = 2\angle ACB\]
\[ \Rightarrow \angle ACB = \dfrac{1}{2}\angle AOB\]………………… (1)

Now from figure it is given that \[\angle AOB = {126^0}\] and \[\angle ACB = x\]
So from equation (1) we have,
\[ \Rightarrow x = \dfrac{1}{2}\left( {{{126}^0}} \right) = {63^0}\]

So this is the required value of the x.

Hence option (B) is correct.

Note: Whenever we face such types of problems the key concept is to have the basic understanding of the diagrammatic representation in order to have a better clarity about the geometry of the figure. This concept along with basic circle properties of geometry will help you get on the right track to get the answer.