Question

In the figure, 'O' is the centre of the circle, ZABO= 20°and ZACO= 30°, where

A, B, C are points on the circle. What is the value of x ?
120​

Answer 1

Given:

Consider the below figure attached with this question.

`\angle ABO=20^\circ`

`\angle ACO=30^\circ`

To find:

The value of x.

Solution:

Draw a line segment OA as shown below.

In triangle ABO,

`OA=OB` [Radii of same circle]

`m\angle BAO=m\angle ABO=20^\circ` [Base angles of an isosceles triangle]

In triangle ACO,

`OA=OC` [Radii of same circle]

`m\angle CAO=m\angle ACO=30^\circ` [Base angles of an isosceles triangle]

Now,

`m\angle BAC=m\angle BAO+m\angle CAO`

`m\angle BAC=20^\circ+30^\circ`

`m\angle BAC=50^\circ`

Central angle is always twice of angle subtended by two points on the circle.

`m\angle BOC=2* m\angle BAC`

`x=2* (50^\circ)`

`x=100^\circ`

Therefore, the value of x is 100°.