Question

In figure, line $PR$ touches the circle at point $Q$. Answer the following with the help of the figure:
What is the sum of $\angle TAQ$ and $\angle TSQ$?

Answer 1

Here, $AQST$ is a cyclic quadrilateral.

We know, in a cyclic quadrilateral, the sum of opposite angles are supplementary, i.e. ${180}^o$.

Here, $\angle A=\angle TAQ$ and $\angle S=\angle TSQ$ are opposite angles.

Then clearly, $\angle A+\angle S={180}^o$

$⟹$ $\angle TAQ+\angle TSQ={180}^o$.

That is the sum of $\angle TAQ$ and $\angle TSQ$ is ${180}^o$.