Question

In the given figure, identify $\angle AOB$

• A. ${75}^{\circ }$
• B. ${85}^{\circ }$
• C. ${95}^{\circ }$
• D. ${105}^{\circ }$

Answer 1

Answer: (D)

${105}^{\circ }$

AOBC is a quadrilateral.

Therefore sum of all four angles should be ${360}^{\circ }$

.

$\angle OBC+\angle OAC+\angle AOB+\angle BCA={360}^{\circ }$

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

${90}^{\circ }+{90}^{\circ }+{75}^{\circ }+\angle AOB={360}^{\circ }$

$\angle AOB={360}^{\circ }-{255}^{\circ }$

$\angle AOB={105}^{\circ }$

So , option D will be the answer.