PLEASE HELP! A student says that the measures of coterminal angles are never opposites of each other. Is the student correct? Explain.

A student says that the measures of coterminal angles are never opposites of each other, the student is wrong because Coterminal angles are angles in standard position (angleswith the initial side on the positive x -axis) that have a common terminal side. For example 30° , −330° and 390° are all coterminal.

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fichoh fichoh · Answer 2 · 2021-11-02T14:17:18+01:00

Based on the properties of coterminal angles, the standard and terminal side are opposite, hence, coterminal angles are opposite each other.

When the terminal side of an angle also occupies the standard position.

The positive angle is located on the x - axis which is rooted to the origin. This is the angle in the standard postion.

Coterminal angles do have identical vertices and the share the same sides, however they posses different angles.

In the attached picture, angle in the standard postion is 45° and the terminal is - 315°

Therefore, the measures of coterminal angles are opposite each other.

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