Multiple Choice
Line is tangent to circle at point . If the measure of angle is , what is the measure of the angle between the tangent and the radius at point ?
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1. Measuring Angles
Angles in Standard Position
Multiple Choice
In standard position, if = , what is the reference angle?
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Verified step by step guidance1
Understand that the reference angle is the acute angle formed between the terminal side of the given angle \( \theta \) and the x-axis.
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.
Recall that for angles in the first quadrant, the reference angle is the angle itself, so the reference angle is \( 53^\circ \).
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.
Therefore, since \( 53^\circ \) is in the first quadrant, the reference angle is simply \( 53^\circ \).
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