Question

asked Jun 24, 2022 179k views

1 Answer

StigM · Answer 1 · 2022-06-28T13:33:41+0000

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.

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