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Pls help me solve pls show how you got the answer

Pls help me solve pls show how you got the answer-example-1

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Given:

The figure of a circle O.

To find:

The value of x.

Solution:

First, label some points on the given figure as shown below.

In triangle BOC,


OB=OC (Radii of same circle)

It means
\Delta BOC is an isosceles triangle and the base angles of an isosceles triangles are congruent. So,


\angle OBC\cong \angle OCB


m\angle OBC=m\angle OCB


75^\circ=m\angle OCB

In triangle
\Delta BOC,


m\angle BOC+m\angle OBC+m\angle OCB=180^\circ (Angle sum property)


m\angle BOC+75^\circ+75^\circ=180^\circ


m\angle BOC+150^\circ=180^\circ


m\angle BOC=180^\circ-150^\circ


m\angle BOC=30^\circ

Now,


m\angle BOC=m\angle BOC+m\angle COD


m\angle BOC=30^\circ+94^\circ


m\angle BOC=124^\circ

Using the central angle theorem, we get


m\angle BAD=(1)/(2)* m\angle BOD


x=(1)/(2)* 124^\circ


x=62^\circ

Therefore, the correct option is B.

Pls help me solve pls show how you got the answer-example-1
User StigM
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