Problem

The angle between $0^{\circ}$ and $360^{\circ}$ and is coterminal with a standard position angle measuring $987^{\circ}$ angle is degrees.
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Answer

First, we subtract $360^\circ$ from $987^\circ$ to get $627^\circ$. This is still greater than $360^\circ$, so we subtract $360^\circ$ again to get $267^\circ$. This is between $0^\circ$ and $360^\circ$, so the angle between $0^\circ$ and $360^\circ$ that is coterminal with $987^\circ$ is $\boxed{267^\circ}$.

Steps

Step 1 :An angle is coterminal with another if they differ by a multiple of $360^\circ$. So, to find the angle between $0^\circ$ and $360^\circ$ that is coterminal with $987^\circ$, we subtract multiples of $360^\circ$ from $987^\circ$ until we get an angle between $0^\circ$ and $360^\circ$.

Step 2 :First, we subtract $360^\circ$ from $987^\circ$ to get $627^\circ$. This is still greater than $360^\circ$, so we subtract $360^\circ$ again to get $267^\circ$. This is between $0^\circ$ and $360^\circ$, so the angle between $0^\circ$ and $360^\circ$ that is coterminal with $987^\circ$ is $\boxed{267^\circ}$.

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