Multiple Choice
Which of the following best describes alternate exterior angles in the context of two parallel lines cut by a transversal?
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1. Measuring Angles
Angles in Standard Position
Multiple Choice
Given a point on the terminal side of an angle in standard position, what is the measure of angle in degrees?
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Verified step by step guidance1
Identify the coordinates of the point on the terminal side of the angle: here, the point is (3, 4).
Recall that the angle in standard position is formed by the positive x-axis and the line segment from the origin to the point (3, 4).
Use the tangent function, which relates the angle \( \theta \) to the ratio of the y-coordinate to the x-coordinate: \( \tan(\theta) = \frac{y}{x} \). Substitute the values: \( \tan(\theta) = \frac{4}{3} \).
To find the angle \( \theta \), take the inverse tangent (arctangent) of \( \frac{4}{3} \): \( \theta = \tan^{-1}\left(\frac{4}{3}\right) \).
Use a calculator set to degree mode to evaluate \( \tan^{-1}\left(\frac{4}{3}\right) \), which will give the measure of the angle in degrees.
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