What angle does the hour hand turn in 30 minutes?

Turning around the dial, the hour hand describes a circle, in which it is the radius. We need to calculate the degree measure of the angle that the arrow travels for 30 minutes.

Circle, its elements
We found out that the arrow describes a circle. A circle is a closed flat figure, which is a collection of points equidistant from a given point (center of the circle) at the same distance. The degree measure of a circle is 360 °. In the problem, we are dealing with three elements of a circle:

radius;
arc;
central corner.

The segment that connects the center of the circle to any point on the boundary of the circle is called its radius (r, R). The radii of the circle are equal to each other.

An arc is a part of a circle, a curve enclosed between two points on the boundary of a circle. The arc length can be calculated using the formula:

L = (2pR * n) / 360 °, where

n ~ 3.14,

R is the radius of the circle,

n is the degree measure of the central angle.

The central angle is the angle formed by two radii of a circle with a vertex at its center.

We calculate the degree measure of the angle in the problem
Let’s execute a drawing for the task that graphically displays the dial as a circle and the minute hand as a radius:

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 a circle with apex 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 °.