1 Answer

Bharat Patil · Answer 1 · 2022-07-11T03:15:44+0000

Given:

A figure of a circle.

To find:

The value of x.

Solution:

First label the given figure as shown below.

In triangle ABO,

OA=OB (Radii of same circle)

$\Delta ABO$ is an isosceles triangle. (By the definition of isosceles triangle)

$\angle OAB\cong \angle OBA$ (Base angles of an isosceles triangle)

$m\angle OAB=m\angle OBA$

$42^\circ=m\angle OBA$

In triangle ABO,

$m\angle AOB+m\angle OAB+m\angle OBA=180^\circ$ (Angle sum property)

$m\angle AOB+42^\circ+42^\circ=180^\circ$

$m\angle AOB=180^\circ-42^\circ-42^\circ$

$m\angle AOB=96^\circ$

Now,

$m\angle AOB+m\angle BOC=180^\circ$ (Linear pair)

$96^\circ+x=180^\circ$

$x=180^\circ-96^\circ$

$x=84^\circ$

Therefore, the value of x is 84 degrees.

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