Question

what is ( moverarc{qs} )?
(there is a circle with center, and three radii to points r, s, q. the arc from r to the top (with s) is 150°, the arc from r to q is 120°. we need to find ( moverarc{qs} ), and there is a box to fill the answer with a degree symbol.)

Explanation:

Step1: Recall circle angle sum

A full circle is \(360^\circ\). Let \(m\angle ROS = 150^\circ\), \(m\angle ROQ = 120^\circ\), and we need \(m\angle QOS\) (which is \(m\overarc{QS}\)).

Step2: Calculate the remaining angle

The sum of angles around the center is \(360^\circ\). So \(m\overarc{QS}=360^\circ - 150^\circ - 120^\circ\).
Calculate \(360 - 150 - 120 = 90\).

Answer:

\(90\)