Video: Finding an Angle around a Point given Its Coterminal Angle

Find the measure of ∠𝜃.

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Find the measure of angle 𝜃.

There’s a few things we should notice here. In this image, there are two angles: angle 50 degrees and angle 𝜃 degrees.

These angles share both their initial side and their terminal side. Together, these two angles measure 360 degrees.

To find angle 𝜃, we take 360 degrees, subtract the 50-degree angle, and find that the measure of angle 𝜃 is equal to 310 degrees.