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,
[tex]OB=OC[/tex] (Radii of same circle)
It means [tex]\Delta BOC[/tex] is an isosceles triangle and the base angles of an isosceles triangles are congruent. So,
[tex]\angle OBC\cong \angle OCB[/tex]
[tex]m\angle OBC=m\angle OCB[/tex]
[tex]75^\circ=m\angle OCB[/tex]
In triangle [tex]\Delta BOC[/tex],
[tex]m\angle BOC+m\angle OBC+m\angle OCB=180^\circ[/tex] (Angle sum property)
[tex]m\angle BOC+75^\circ+75^\circ=180^\circ[/tex]
[tex]m\angle BOC+150^\circ=180^\circ[/tex]
[tex]m\angle BOC=180^\circ-150^\circ[/tex]
[tex]m\angle BOC=30^\circ[/tex]
Now,
[tex]m\angle BOC=m\angle BOC+m\angle COD[/tex]
[tex]m\angle BOC=30^\circ+94^\circ[/tex]
[tex]m\angle BOC=124^\circ[/tex]
Using the central angle theorem, we get
[tex]m\angle BAD=\dfrac{1}{2}\times m\angle BOD[/tex]
[tex]x=\dfrac{1}{2}\times 124^\circ[/tex]
[tex]x=62^\circ[/tex]
Therefore, the correct option is B.
