Finding an Angle Coterminal with an Angle of Measure Greater Than 360°

Find the least positive angle $θ$ that is coterminal with an angle measuring $800°,$ where $0° \leq θ < 360 ° .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
An angle with measure $800°$ is coterminal with an angle with measure $800 - 360 = 440°,$ but $440°$ is still greater than $360°,$ so we subtract $360°$ again to find another coterminal angle: $440 - 360 = 80° .$
The angle $θ = 80°$ is coterminal with $800° .$ To put it another way, $800°$ equals $80°$ plus two full rotations, as shown in Figure 18.

Figure 18

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find an angle $α$ that is coterminal with an angle measuring $870°,$ where $0° \leq α < 360° .$

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