Challenges on Cyclic Quadrilaterals

Q.

Find the sum of the interior angles of any quadrilateral, by dividing it into two triangles.

Q. The opposite angles of a cyclic quadrilateral is in the ratio $2:3.$ Find the angles.

1. ${36}^o$
2. ${144}^o$
3. ${72}^o$
4. ${108}^o$

Q. Evaluate $x$ and $y$ for the given cyclic quadrilateral.

1. $x=\frac{{46}^o}{3},y=\frac{{227}^o}{6}$
2. $x={46}^o,y={227}^o$

Q. Two sides XY and YZ of the inscribed quadrilateral is equidistant from the center of the circle with radius √32 units. The length of XY is 8 units. Find the angle ∠W.
degrees

Q. For the given figure, find the angle $\angle XWU.$

1. ${89}^o$
2. ${90}^o$
3. ${91}^o$