Challenges on Quadrilaterals formed by Intersection of Two Circles

Q. In the given figure if $\angle ADC={110}^{\circ },$ then $\angle ABC=$

1. ${40}^{\circ }$
2. ${50}^{\circ }$
3. ${60}^{\circ }$
4. ${30}^{\circ }$

Q. A quadrilateral is formed by intersecting two circles, such that two vertices of the quadrilateral lie on each circle. If one angle of the quadrilateral is right angle, comment on the properties of the quadrilateral.

1. Two sides are parallel to each other.
2. The quadrilateral has two right angles.
3. The sum of opposite angles is ${180}^o.$
4. The sum of adjacent angles is ${180}^o.$

Q. Find the relation between the angles $\angle X$ and $\angle Y.$

1. $\angle Y={180}^o-\angle X$
2. $\angle Y={90}^o-\angle X$
3. They are supplementary angles.
4. Nothing cannot be said without sufficient data.

Q. For the given figure, find the angle ∠ZVY.

degrees.

Q. For the given figure, determine the angle ∠P.

degrees

Q. In the given figure $m\angle A={84}^{\circ },m\angle B={80}^{\circ },$ then

1. $m\angle C={96}^{\circ },m\angle D={100}^{\circ }$
2. $m\angle C={100}^{\circ },m\angle D={96}^{\circ }$
3. $m\angle C={100}^{\circ },m\angle D={100}^{\circ }$
4. $m\angle C={96}^{\circ },m\angle D={96}^{\circ }$

Q. Two circles intersect at $\text{B}$ and $\text{E}$. Quadrilaterals $\text{ABEF}$ and $\text{BCDE}$ are inscribed in these circles such that $\text{ABC}$ and $\text{FED}$ are line segments. Also, $\angle \text{A}={96}^{\circ }$ and $\angle \text{F}={75}^{\circ }$, the value of $x$ is:

1. ${96}^{\circ }$
2. ${84}^{\circ }$
3. ${75}^{\circ }$
4. ${105}^{\circ }$