Angle Subtended by an Arc of a Circle

$ABCDE$ is a pentagon inscribed in a circle, If$AB=BC=CD$ and  $\angle BCD={110}^0, \angle BAE={120}^0,$ find $\angle EAD$.

$ABCDE$ is a pentagon inscribed in a circle, If $AB=BC=CD$ and  $\angle BCD={110}^0, \angle BAE={120}^0,$ find $\angle AED$.

$ABCDE$ is a pentagon inscribed in a circle, If $AB=BC=CD$ and  $\angle BCD={110}^0, \angle BAE={120}^0,$ find $\angle CDE$.

$ABCDE$ is a pentagon inscribed in a circle, If $AB=BC=CD$ and  $\angle BCD={110}^0, \angle BAE={120}^0,$ find $\angle ABC$.

In given circle with centre $O$, the lengths of arc $PQ$ and arc $QR$ are in the ratio $3 : 2. \mathrm{If} \angle POQ = {96}^0,$ find $\angle PSQ$

In given circle with centre $O$, the lengths of arc $PQ$ and arc $QR$ are in the ratio $3 : 2. \mathrm{If} \angle POQ={96}^0,$ find $\angle RPQ$

In given figure, PQ is a side of a regular hexagon and PR is the side of a regular octagon inscribed in a circle with centre O. Calculate the measures of $\angle PQR$.

In Fig. $13.47,$  PQ is a side of a regular hexagon and PR is the side of a regular octagon inscribed in a circle with centre O. Calculate the measures of $\angle PRQ$

In given figure, PQ is a side of a regular hexagon and PR is the side of a regular octagon inscribed in a circle with centre O. Calculate the measures of $\angle POQ$

In a regular pentagon $ABCDE$ inscribed in a circle, find the ratio between $\angle EDA$ and $\angle ADC$.

(Answer in the form $\frac{a}{b}$)

In given figure, chord $PQ=$ chord $RQ$. If $\angle POQ = 40°$, find the measure of $\angle QPR$.

$PQ$ is a diameter of the circle with centre $O$. If chord $PR=$chord $PS$, arc $PR=2$ arc $QR$, find $\angle PQR$.

$PQ$ is a diameter of the circle with centre $O$. If chord $PR=$chord $PS$, arc $PR=2$ arc $QR$, find $\angle QPR$.

Draw a triangle of circumradius $3 \mathrm{cm}$ and two of the angles $32\frac{1}{2}°$ and $37\frac{1}{2}°$.

In the given figure, the two circles with centres $P$ and $Q$ intersect at $A$ and $B$. $Q$ lies on the circumference of the bigger circle. If $\angle APB=60°$, then find $\angle ARB$.

In the given figure, $AD$ is a diameter and $O$ is the center of the circle $AD$ is parallel to $BC$ and $\angle CBD=32°$.

Find $\angle BED$.

In the given figure, $AD$ is a diameter and $O$ is the center of the circle $AD$ is parallel to $BC$ and $\angle CBD=32°$.

Find $\angle AOB$.

In the given figure, $AD$ is a diameter and $O$ is the centre of the circle $AD$ is parallel to $BC$ and $\angle CBD=32°$.

Find $\angle OBD$

In the figure given below, '$O$' is the center of the circle. If $QR=OP$ and $\angle ORP=20°$. Find the value of '$x$' giving reasons.

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Find the value of unknown variables in the following.