Question

In the given figure 'O' is the center of the circle. SP and TP are the two tangents at S and T respectively. $\angle SPT$ is ${50}^{\circ }$, the value of $\angle SQT$ is:

• A. 125°
• B. 65°
• C. 115°
• D. None of the above

Answer 1

The correct option is C

115°

$\angle OSP$ =$\angle OTP$ = ${90}^{\circ }$
Since the angles in a quadrilateral add up to ${360}^{\circ }$, and three angles are ${90}^{\circ }$, ${90}^{\circ }$ and ${50}^{\circ }$, the 4th angle would be ${130}^{\circ }$.
$\angle SPT$+ $\angle SOT$ = ${180}^{\circ }$

$\angle SOT$ = ${130}^{\circ }$

The reflex angle, $\angle SOT$ = ${360}^{\circ }$– ${130}^{\circ }$ = ${230}^{\circ }$

$\angle SQT$ = $\frac{1}{2}$ $\times$reflex angle $\angle SOT$

$\angle SOT$ = $\frac{1}{2}$ $\times$ ${230}^{\circ }$

$\angle SOT$ = ${115}^{\circ }$