Question

In the cyclic quadrilateral WXYZ on the circle centred at O, $\angle ZYW={10}^{\circ }$ and $\angle YOW={100}^{\circ }$. What is the measure of $\angle YWZ$?

• A. ${30}^{\circ }$
• B. ${40}^{\circ }$
• C. ${50}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${40}^{\circ }$

Since $\angle YXW$ is an inscribed angle it is equal to $\frac{1}{2}\times 100={50}^{\circ }$ . In a cyclic quadrilateral, opposite angles sum up to ${180}^{\circ }$, so $\angle YZW=180-50={130}^{\circ }$ . Consider $\Delta YWZ,$ The interior angles of a triangle sum up to ${180}^{\circ }$ , so $\angle YWZ=180-10-130={40}^{\circ }$.