Question

In the adjoining figure, $AT$ is a tangent at $A$. If $\angle TAB={75}^o$ and $\angle BAC={40}^o$, find $\angle ABC$.

• A. ${90}^o$
• B. ${45}^o$
• C. ${75}^o$
• D. ${65}^o$

Answer 1

The correct option is D ${65}^o$

A chord and a tangent intersect externally.
So, according to the segment theorem, angle between the tangent and chord at the point of contact is equal.
So, $\angle TAB=\angle ACB=75$
Sum of the triangle, $180=40+75+\angle ABC$
$\angle ABC=180-115$
$\angle ABC={65}^o$