Question

In the above figure, $\angle CAB={60}^{\circ },\angle CBA={60}^{\circ }$. PQ is a tangent at A. What is the value of $\angle BAQ$.

• A. ${60}^{\circ }$
• B. ${20}^{\circ }$
• C. ${40}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is A

${60}^{\circ }$

In $\Delta ABC,$
$\angle CBA+\angle CAB+\angle ACB={180}^{\circ }$ [Sum of angles in a triangle is equal to ${180}^{\circ }$]
${60}^{\circ }+{60}^{\circ }+\angle ACB={180}^{\circ }$
$\Rightarrow {120}^{\circ }+\angle ACB={180}^{\circ }\angle ACB={180}^{\circ }-{120}^{\circ }\angle ACB={60}^{\circ }$
But, $\angle ACB=\angle BAQ$ [Angle in an alternate segment are equal]
[The angle between the tangent and a chord through the point of contact is equal to an angle in the alternate segment]
$\therefore \angle ACB=\angle BAQ={60}^{\circ }$