Question

In the above figure, $\angle p+\angle q=$ .

• A. ${12}^{\circ }$
• B. ${52}^{\circ }$
• C. ${72}^{\circ }$
• D. ${92}^{\circ }$

Answer 1

The correct option is D ${92}^{\circ }$

On joining A to B and C to D, AB and CD will become chords.


We know that the angles subtended by the same chord in the same segment are equal.
$⟹\angle CAD=\angle CBD$ and
$\angle ACB=\angle ADB.$
$⟹{52}^{\circ }=\angle p$ and
${40}^{\circ }=\angle q.$
$\therefore \angle p+\angle q={52}^{\circ }+{40}^{\circ }={92}^{\circ }$