Circle Practice Questions with Solutions – Level 2

In a cyclic quadrilateral $ABCD$, $\angle A = (3x + 15)^\circ$ and $\angle C = (x + 25)^\circ$. Find the measure of $\angle A$.

In cyclic quadrilateral $ABCD$, the ratio of angles $\angle A : \angle B : \angle C = 2 : 3 : 7$. What is the measure of $\angle D$?

In a cyclic quadrilateral $ABCD$, side $AB$ is a diameter of the circumcircle. If $\angle ADC = 130^\circ$, find the measure of $\angle BAC$.

Quadrilateral $ABCD$ is inscribed in a circle. If $\angle A = 2\angle C$ and $\angle B = 3\angle D$, what is the measure of $\angle B$?

In cyclic quadrilateral $ABCD$, $AB \parallel CD$. If $\angle A = 70^\circ$, what is the measure of $\angle B$?

In a cyclic quadrilateral $ABCD$, side $AB$ is extended past $B$ to point $E$. If exterior angle $\angle CBE = 115^\circ$, what is the measure of interior angle $\angle ADC$?

In cyclic quadrilateral $ABCD$, side $BC$ is extended to $F$. If $\angle DCF = (2x + 10)^\circ$ and $\angle BAD = (3x - 20)^\circ$, find the value of $x$.

Side $AB$ of cyclic quad $ABCD$ is extended to $E$. If $\angle CBE = 85^\circ$ and $\angle BAC = 35^\circ$, what is the measure of $\angle BDC$?

In cyclic quadrilateral $ABCD$, side $AD$ is extended to $G$. If exterior angle $\angle CDG = 100^\circ$ and $\angle DBC = 40^\circ$, find $\angle ABD$.

Sides $AB$ and $DC$ of a cyclic quadrilateral $ABCD$ are extended to meet at point $P$. If exterior angle $\angle PBC = 75^\circ$ and $\angle PCB = 50^\circ$, find $\angle ADC$.