Cyclic Quadrilateral and its Property

Q.

Find the size of the each of the angle marked with the letter in the diagram. Equal sides are marked by the dashes and parallel sides are marked by double arrows.

Q. The opposite angles of a quadrilateral inscribed in a circle are -

1. complementary anlges
2. supplimentary angles
3. co-interior angles
4. alternate interior angles

Q. One side of a cyclic quadrilateral passes through the center of a circle. A pair of opposite sides of the quadrilateral is parallel. Determine the angle $\angle XWZ.$

1. ${65}^o$
2. ${100}^o$
3. ${115}^o$

Q. A cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single -

1. tetrahedron
2. pentagon
3. ellipse
4. circle

Q. Given that $\angle \text{PQR}={100}^{\circ }$. If $\angle \text{POR}={80}^{\circ }$, then quadrilateral $\text{OPQR}$ is a cyclic quadrilateral.

1. False
2. True

Q. The radius of a circle is equal to the chord of a circle. The chord's angle at a position on the major arc and at a position on the minor arc are

1. ${30}^{\circ },{150}^{\circ }$
2. ${150}^{\circ },{30}^{\circ }$
3. ${60}^{\circ },{120}^{\circ }$
4. ${120}^{\circ },{60}^{\circ }$

Q. For the given figure, P is the center of the circle.
Find the ∠XWZ.


degrees

Q.

A quadrilateral has three acute angles. If each measures $80°$, then the measure of the fourth angle is

1. $150°$

2. $120°$

3. $105°$

4. $140°$

Q. Find the possible pairs of the opposite angles for a inscribed quadrilateral.

1. ${110}^o,{70}^o$
2. ${65}^o,{25}^o$
3. ${11}^o,{169}^o$
4. ${123}^o,{69}^o$

Q. The sum of either pair of opposite angles of a quadrilateral inscribed in a circle is ${90}^{\circ }$

1. True
2. False