Constructing a segment of a circle subtending a given angle

In this exercise you are given an angle \(\angle XYZ\). Your task is to construct a segment of the circle with one end at \(R\) which subtends the angle \(\angle XYZ\) on the circle. Once you have finished the construction, you can use the angle measurement tool to confirm that the angle is the correct size. You may find the exercise on transferring an angle very useful!

In the diagram below you can see an example. The angle \(\angle DEF\) is given, and in the circle the segment \(AC\) subtends an angle \(\angle ABC\) equal to \(\angle DEF\).