Central and Inscribed Angles — Practice Set

In a circle, the arc intercepted by a central angle measures 84°. What is the measure of the central angle?

A circle has a total arc measure of 360°. A central angle of 120° intercepts minor arc $PQ$. What is the measure of major arc $PQ$?

An angle has its vertex on a circle and its two sides are chords. What type of angle is this?

Circle $O$ has center $O$. Central angle $AOB = 130\degree$. What is the measure, in degrees, of minor arc $AB$?

In circle $O$, central angle $MON = 210\degree$. What is the measure, in degrees, of minor arc $MN$?

An inscribed angle intercepts an arc of 96°. What is the measure, in degrees, of the inscribed angle?

Inscribed angle $ACB$ measures 37°. What is the measure, in degrees, of intercepted arc $AB$?

Points $A$, $B$, $C$, and $D$ lie on a circle in that order. Inscribed angle $ACB = 55\degree$ and inscribed angle $ADB$ both intercept arc $AB$ (the arc not containing $C$ or $D$). What is the measure of angle $ADB$?

In circle $O$, central angle $POQ = 88\degree$. Inscribed angle $PRQ$ also intercepts arc $PQ$. What is the measure of inscribed angle $PRQ$?

Points $X$, $Y$, $Z$, and $P$ lie on a circle in that order. Arc $XY = 140\degree$ and arc $YZ = 80\degree$. Point $P$ is on arc $ZX$ (the remaining arc). Arc $ZX = $   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   degrees. Inscribed angle $XPZ$, whose vertex is $P$ and which intercepts arc $XYZ$ (the arc from $X$ to $Z$ going through $Y$), measures   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   degrees.

In circle $O$, the major arc $ST = 260\degree$. Inscribed angle $SUT$ has its vertex $U$ on the major arc, so it intercepts the minor arc $ST$. What is the measure of angle $SUT$?

Point $P$ is inside circle $O$ (not on the circle). Two chords pass through $P$, forming an angle of 40° at $P$. A student claims this is an inscribed angle intercepting an arc of 80°. What error did the student make?

Points $A$ and $B$ are the endpoints of a diameter of circle $O$. Point $C$ lies on the circle. What is the measure, in degrees, of inscribed angle $ACB$?

A rider at point $C$ on the rim of the Ferris wheel sits on the major arc — the longer arc not directly between seats $A$ and $B$. What is the measure, in degrees, of inscribed angle $ACB$?

The designer wants to place a bench at $R$ so that the angle $PRQ$ (the view angle from the bench to points $P$ and $Q$) equals 55°. What is the measure of inscribed angle $PRQ$?

What is the diameter of the circle, in centimeters?

What error did Jordan make?

Is Sam's work correct? If not, identify the error.

In circle $O$, central angle $AOB = 124\degree$. Point $C$ is on the major arc. Point $D$ is on the minor arc. Inscribed angle $ADB$ intercepts the major arc $AB$. What is the measure, in degrees, of inscribed angle $ADB$?

Quadrilateral $ABCD$ is inscribed in a circle (a cyclic quadrilateral). Angle $A = 73\degree$. What is the measure, in degrees, of angle $C$?