Question

In the given quadrilateral $OQPR,$ if $\angle QPR={50}^{\circ }$ then $\angle QOR$ equals

• A. ${120}^{\circ }$
• B. ${130}^{\circ }$
• C. ${145}^{\circ }$
• D. ${110}^{\circ }$

Answer 1

Answer: (B)

${130}^{\circ }$

Tangent is perpendicular to the radius at the point of contact.

Therefore, $\angle OQP=\angle ORP={90}^{\circ }$

Sum of all the four interior angles of a quadrilateral is ${360}^{\circ }.$ So,

$\angle PQO+\angle QOR+\angle ORP+\angle RPQ={360}^{\circ }$

$\Rightarrow {90}^{\circ }+\angle QOR+{90}^{\circ }+{50}^{\circ }={360}^{\circ }$ [Given $\angle RPQ={50}^{\circ }$]

$\Rightarrow \angle QOR={130}^{\circ }$

Hence, option $B$ is correct.