Name: Degrees and radians: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 27 s
Description: An angle measures 150°. What is the measure of this angle in radians? Try it, then watch the animated solution.

Degrees and radians measure the same turn. A half turn is

180^\circ

, and it is also

\pi

radians.

To change degrees to radians, multiply by

\tfrac{\pi}{180^\circ}

:

150^\circ \cdot \tfrac{\pi}{180^\circ} = \tfrac{150\pi}{180}

.

Divide top and bottom by

30

:

\tfrac{150\pi}{180} = \tfrac{5\pi}{6}

. The angle is

5

of the

6

equal slices of the half turn.

Traps:

\tfrac{2\pi}{3}

is

120^\circ

,

\tfrac{6\pi}{5}

flips the fraction, and

\tfrac{5\pi}{3}

uses

2\pi

for the half turn.

Try it first