What angle does the hour hand turn in 30 minutes?

In the drawing, AO and BO are the radii of the circle: AO = BO = r.

Between the radii AO and BO lies the central angle ∠AOB of the circle with the vertex at point O. Between points A and B on the circle, there is an arc .AB.

It is necessary to find the degree measure of the angle AOB. As we know, the degree measure of a circle leaves 360 °. The hour hand rotates 360 ° in 60 minutes. This means that in 1 minute the arrow moves to:

360 °: 60 = 6 °.

Then in 30 minutes it will move to:

6 ° * 30 = 180 °.

Thus, in 30 minutes, the arrow moves 180 °, describing a semicircle and forming an extended angle.

Answer: 180 °.