Question

In the given figure, $POQ$ is the diameter of the circle with centre O. What is the value of $x+y$?

• A. ${120}^{\circ }$
• B. ${270}^{\circ }$
• C. ${250}^{\circ }$
• D. ${200}^{\circ }$

Answer 1

The correct option is B ${270}^{\circ }$

As angle subtended by the diameter as a chord on the circumference is ${90}^{\circ }$

$\Rightarrow \angle PTQ={90}^{\circ }$

As $\angle STQ$ and $\angle SRQ$ are opposite angles of quadrilateral $\left(TSRQ\right)$

$\therefore \angle STQ+\angle SRQ={180}^{\circ }$

$\to x+y=\angle PTQ+\angle STQ+\angle SRQ={90}^{\circ }+{180}^{\circ }={270}^{\circ }$