Question

In the figure below XYQZ is a quadrilateral with its vertices on a circle and XYZ is an equilateral triangle. Find the value of $\angle$ YQZ.

• A. ${70}^{\circ }$
• B. ${120}^{\circ }$
• C. ${60}^{\circ }$
• D. ${110}^{\circ }$

Answer 1

The correct option is B

${120}^{\circ }$

$\angle YXZ={60}^{\circ }$ (as $\Delta XYZ$ is an equilateral triangle)

XYQZ is a cyclic quadrilateral

$\therefore \angle YXZ+\angle YQZ={180}^{\circ }$

$60+\angle YQZ={180}^{\circ }$

$\angle YQZ={120}^{\circ }$