Textbook Question
Give two positive and two negative angles that are coterminal with the given quadrantal angle. 0°
820
views
1. Measuring Angles
Coterminal Angles
Multiple Choice
Which of the following is a measure of an angle that is coterminal with ?
A
B
C
D
Verified step by step guidance1
Recall that two angles are coterminal if they differ by a full rotation of 360 degrees, meaning their measures differ by multiples of 360°.
To find angles coterminal with 135°, add or subtract multiples of 360° to 135°. This can be expressed as: \(\theta = 135° + 360° \times k\), where \(k\) is any integer.
Calculate a few examples by substituting values for \(k\): for \(k=1\), \(\theta = 135° + 360° = 495°\); for \(k=2\), \(\theta = 135° + 720° = 855°\); for \(k=-1\), \(\theta = 135° - 360° = -225°\).
Compare the given options (90°, 495°, 585°, 45°) to the values obtained by adding or subtracting 360° multiples from 135° to identify which is coterminal.
Conclude that the angle measure that matches the form \(135° + 360° \times k\) for some integer \(k\) is coterminal with 135°.
Related Videos
Related Practice
