Inscribed Angles: Practice

Diameter $VD$ is outside $\angle AVB$, with ray $VA$ between $VD$ and $VB$. Angle $DVB$ measures $71^\circ$, and $DVA$ measures $26^\circ$. Find arc $AB$ excluding $V$.

Diameter $VD$ lies inside $\angle AVB$. Angles $AVD$ and $DVB$ measure $(x+7)^\circ$ and $(2x-4)^\circ$. The intercepted arc $ADB$ measures $174^\circ$. Find $x$.

$VA$ is a diameter with center $O$. In triangle $VOB$, the angle at $O$ measures $(4x+12)^\circ$, and the angle at $B$ measures $(x+6)^\circ$. Find arc $BA$ excluding $V$.

Point $Q$ lies on major arc $AB$, and $R$ lies on minor arc $AB$. Given $m\angle AQB=82^\circ$ and arc $AR$ of $76^\circ$, find arc $RB$ along minor arc $AB$.

An inscribed angle measures $(4x+30)^\circ$. Its intercepted major arc measures $(7x+80)^\circ$. Find $x$.

Triangle $ABC$ is inscribed in a circle and has a right angle at $C$. Its angles at $A,B$ measure $(4x+8)^\circ$ and $(6x+2)^\circ$. Find arc $AC$ excluding $B$.

Opposite tangent rays $TR,TS$ form angles with chord $TA$ of $(3x+11)^\circ$ and $(5x+9)^\circ$, respectively. Ray $TR$ lies on the same side of line $OT$ as $A$. Find minor arc $TA$.

Ray $TS$ is tangent at $T$ on the opposite side of line $OT$ from $A$. Given $m\angle STA=94^\circ$, point $B$ on major arc $TA$, and $m\angle TAB=31^\circ$, find $m\angle ATB$.

$P$ lies on major arc $AB$, and $Q$ on minor arc $AB$. Given $m\angle APB=62^\circ$, what is the measure of arc $APB$ containing $P$?

Diameter $VD$ is inside $\angle AVB$. Angle $AVB$ measures $81^\circ$, and arc $AD$ measures $68^\circ$. Find arc $DB$ on intercepted arc $ADB$.

Diameter $VD$ lies outside $\angle AVB$. The arc order away from $V$ is $D,A,B$. Given $m\angle AVB=34^\circ$ and arc $DB$ of $158^\circ$, find arc $DA$.

At $A$, tangent ray $AS$ lies on the opposite side of line $OA$ from $B$, and $m\angle SAB=114^\circ$. Point $P$ lies on major arc $AB$ and $Q$ on minor arc $AB$. Which pair is correct?