AB and AC are two tangents to a circle having centres at the point X. What will be the measure of ∠BAC, if ∠BXC = 125°?

The correct option is 55°.

Step-by-Step Explanation:

Let us analyze the geometric properties given in the problem:

1. We are given a circle centered at point $X$.

2. $AB$ and $AC$ are two tangents drawn from an external point $A$ to the circle, touching the circle at points $B$ and $C$ respectively.

3. The radius of a circle is always perpendicular to the tangent at the point of contact. Therefore:

$\angle ABX=90°$
$\angle ACX=90°$

4. Now, consider the quadrilateral $ABXC$. The sum of all interior angles of a quadrilateral is $360°$.

$\angle BAC+\angle ABX+\angle BXC+\angle ACX=360°$

5. Substitute the known values ($\angle ABX=90°$, $\angle ACX=90°$, and $\angle BXC=125°$) into the equation:

$\angle BAC+90°+125°+90°=360°$

$\angle BAC+305°=360°$

$\angle BAC=360°-305°$

$\angle BAC=55°$

Thus, the measure of $\angle BAC$ is 55°.