In standard position, if $\theta$ = $53°$, what is the reference angle?

• A. $127°$
• B. $53°$
• C. $233°$
• D. $37°$

Answer: (B)

Verified step by step guidance

1. Understand that the reference angle is the acute angle formed between the terminal side of the given angle \( \theta \) and the x-axis.
2. Identify the quadrant in which the angle \( \theta = 53^\circ \) lies. Since \( 53^\circ \) is between \( 0^\circ \) and \( 90^\circ \), it lies in the first quadrant.
3. Recall that for angles in the first quadrant, the reference angle is the angle itself, so the reference angle is \( 53^\circ \).
4. If the angle were in other quadrants, you would calculate the reference angle by subtracting \( \theta \) from \( 180^\circ \), \( 180^\circ \) from \( \theta \), or \( 360^\circ \) from \( \theta \), depending on the quadrant.
5. Therefore, since \( 53^\circ \) is in the first quadrant, the reference angle is simply \( 53^\circ \).