Arcs & Angles in Circles (Set 2) Worksheet

Sample problems

A central angle equals the measure of its intercepted arc; an inscribed angle equals half its intercepted arc. Opposite angles of a quadrilateral inscribed in a circle are supplementary, and a tangent meets a radius at a right angle at the point of tangency. For a circle of radius $r$, an arc with central angle ${\theta }^{\circ }$ has length $\frac{\theta }{360}\cdot 2\pi r$, and the sector has area $\frac{\theta }{360}\cdot \pi r^2$. Leave arc-length and sector-area answers in terms of $\pi$.

1. 1. A central angle of a circle measures $105^{\circ }$. What is the measure of its intercepted arc?
2. 2. An inscribed angle intercepts an arc of $150^{\circ }$. Find the measure of the inscribed angle.
3. 3. An inscribed angle measures $28^{\circ }$. Find the measure of the arc it intercepts.
4. 4. In the circle, $O$ is the center. Find the measure of arc $CD$.

Plus 10 more problems and a full answer key in the PDF.