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Need help w question in this pic thanks!!

Need help w question in this pic thanks!!-example-1
User Nonouco
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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.

Need help w question in this pic thanks!!-example-1
User Bharat Patil
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