Question

which expression finds the measure of an angle that is coterminal with a 45° angle?
45° + 90°
45° + 180°
45° + 270°
45° + 360°

Explanation:

Step1: Recall coterminal angle definition

Coterminal angles are found by adding or subtracting multiples of \(360^\circ\) (for degree measure) because a full rotation is \(360^\circ\). So, the formula for a coterminal angle with an angle \(\theta\) is \(\theta + k\cdot360^\circ\) or \(\theta - k\cdot360^\circ\) where \(k\) is an integer.

Step2: Analyze each option

• Option 1: \(45^\circ + 90^\circ\): This is adding \(90^\circ\), not a multiple of \(360^\circ\), so not coterminal.
• Option 2: \(45^\circ + 180^\circ\): Adding \(180^\circ\), not a multiple of \(360^\circ\), not coterminal.
• Option 3: \(45^\circ + 270^\circ\): Adding \(270^\circ\), not a multiple of \(360^\circ\), not coterminal.
• Option 4: \(45^\circ + 360^\circ\): Here, we are adding \(360^\circ\) (a multiple of \(360^\circ\) with \(k = 1\)), so this will give a coterminal angle.

Answer:

\(45^\circ + 360^\circ\) (the option with \(45^\circ + 360^\circ\))