Cyclic Quadrilaterals

$PQRS$ is a cyclic quadrilateral such that $PR$ is a diameter of the circle. If $\angle QPR=67°$ and $\angle SPR=72°$, $\angle QRS=$

$ABCD$ is a  cyclic quadrilateral where $\angle DBC=27°, \angle ABD=50°$ and $\angle ADB=33°$, then find $\angle ADC$ in degree $\left(°\right)$.

Prove that cyclic parallelogram is always a rectangle.

Prove that any non-isosceles trapezium is not cyclic.

In the given figure some angles are represented by $x, y$ and $z$. Find the values of these angles.

The exterior angle formed by increasing side of a quadrilateral is equal to interior opposite angle. Then, this is a _____ quadrilateral.

In figure, $AOB$  is the diameter of a circle and $C,D \text{and} E$ are three points situated on semi circle. The value of $\angle ACD+\angle BED=$_____$°$

In the given figure, $\mathrm{C}$ and $\mathrm{D}$ are points on the semi-circle described on $\mathrm{AB}$ as diameter. Given that, angle $\mathrm{BAD} = 70°$ and angle $\mathrm{DBC} = 30°$, then calculate angle $\mathrm{BDC}.$

If the given figure, $\mathrm{O}$ is the centre of the circle. The tangents at $\mathrm{B}$ and $\mathrm{D}$ intersect each other at point $\mathrm{P}.$ If $\mathrm{AB}$ is parallel to $\mathrm{CD}$ and $\angle \mathrm{ABC}=55º,$ find $\angle \mathrm{BPD}$.

$\mathrm{ABCDE}$ is a cyclic pentagon with centre of its circumcircle at point $\mathrm{O}$ such that $\mathrm{AB}=\mathrm{BC}=\mathrm{CD}$ and angle $\mathrm{ABC}=120°$. Calculate $\angle \mathrm{BED}$.

Consider the given figure.

The measure of ∠ L + ∠ M + ∠ N + ∠ P = _____ degrees.

In the given figure, P, Q, R, S and T are points lying on the circumference of the circle. O is the centre and PT is the diameter of the circle.

The value of ∠ PQR + ∠RST = _____ degrees.

If O is the centre of the circle and side PQ is produced to R, then the measure of ∠ SQR = _____ degrees.

In the given figure, $ ∆$ IJK is an isosceles triangle with IJ = IK.

The measure of ∠ JLK = _____ degrees.

In the figure given, O is the centre of the circle and L, M, N and P are points on the circumference of the circle. LP is the diameter of the circle.

The measure of ∠ PLN = _____ degrees.

In the figure given, O is the centre of the circle and P, Q and R are points lying on the circumference of the circle.

The measure of ∠ PRQ = _____ degrees.

In the figure below, points $A, B, C$ and $D$ lie on the circle. The measures of $\angle AEC$ and $\angle CBE$ are ${45}^o$ and ${85}^o$ respectively.

The measure of $\angle BAD =$ _____ degrees.

Two circles intersect in point $\mathrm{P}$ and $\mathrm{Q}$. A secant passing through $\mathrm{P}$ intersects the circles in $\mathrm{A}$ and $\mathrm{B}$ respectively. Tangents to the circles at $\mathrm{A}$ and $\mathrm{B}$ intersect at $\mathrm{T}$. Prove that $\mathrm{A},\mathrm{Q},\mathrm{B}$ and $\mathrm{T}$ lie on a circle.