If a pair of opposite angles of a quadrilateral is complementary, then the quadrilateral is cyclic quadrilateral

In the figure, points $P,Q,R$ and $S$ lie on a circle. Then the values of $x$ and $y$ are respectively

In figure $PQ$, is a chord of a circle with centre $O$ and $PT$ is its tangent at $P$. if $\angle QPT=60°$, then $\angle PRQ$ is

The sum of pairs of opposite angles of a cyclic quadrilateral is

$\angle x=$_____$°$

The unknown angle $\angle x=$_____$°$

In the figure $\square \mathrm{PQRS}$ is cyclic. Side $\mathrm{PQ}\cong$Side $\mathrm{RQ}.\angle \mathrm{PSR}=110°$ find $\mathrm{m}(\mathrm{arc} P\mathrm{QR})$

In the given figure, altitudes $\mathrm{YZ}$ and $\mathrm{XT}$ of $\mathrm{\Delta WXY}$ intersect at $\mathrm{P}$. Prove that, $\square \mathrm{WZPT}$ is cyclic.

In the given figure, sides $\mathrm{AD}$ and $\mathrm{AB}$ of cyclic quadrilateral $\mathrm{ABCD}$ are produced to $\mathrm{E}$ and $\mathrm{F}$ respectively.

If$\angle \mathrm{CBF}=130°\text{ and }\angle \mathrm{CDE}=x°$ find the value of $\mathrm{x}$

In the given figure, $△ABC$ is an isosceles triangle in which  $AB=AC$ and a circle passing through $B$ and $C$ intersects $AB$ and $AC$ at $D$ and $E$ respectively.

Prove that $DE\parallel BC$.

In a cyclic quadrilateral $ABCD$, if $\left(\angle B-\angle D\right)=60°$, show that the smaller of the two is $60°$.

In the given figure, $\mathrm{AB}$ is a diameter of a circle with center $\mathrm{O}$ and $\mathrm{DO}\parallel \mathrm{CB}$. If $\angle \mathrm{BCD}=120°$ calculate $\angle \mathrm{ADC}$

$\mathrm{AC}$and $\mathrm{BD}$are chords of a circle which bisect each other. Prove that $\mathrm{ABCD}$ is a rectangle.

Is the picture given a tessellation?