Given that angle is in standard position and its terminal side passes through the point , what is the measure of angle to the nearest degree?
Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
- OLD 1. Angles and the Trigonometric Functions Coming soon
- OLD 2. Trigonometric Functions graphs, Inverse Trigonometric Functions Coming soon
- OLD 3. Trigonometric Identities and Equations Coming soon
- OLD 4. Laws of Sines, Cosines and Vectors Coming soon
- OLD 5. Complex Numbers, Polar Coordinates and Parametric Equations Coming soon
- NEW (not used) 7. Laws of Sines, Cosines and Vectors Coming soon
- NEW (not used) 8. Vectors Coming soon
- NEW(not used) 9. Polar equations Coming soon
- NEW (not used) 11. Graphing Complex Numbers Coming soon
1. Measuring Angles
Angles in Standard Position
Multiple Choice
If angle is a straight angle and bisects angle , what is the measure of angle ?
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Verified step by step guidance1
Understand that angle \( \angle MON \) is a straight angle, which means its measure is \( 180^\circ \).
Recognize that \( \angle MON \) bisects \( \angle MOQ \), meaning \( \angle MON \) divides \( \angle MOQ \) into two equal parts.
Express the relationship: if \( \angle MON \) bisects \( \angle MOQ \), then \( \angle MON = \frac{1}{2} \times \angle MOQ \).
Since \( \angle MON = 180^\circ \), set up the equation \( 180^\circ = \frac{1}{2} \times \angle MOQ \) and solve for \( \angle MOQ \).
Use the value of \( \angle MOQ \) to find \( \angle MOP \) by subtracting the known angles or using the given relationships in the figure.
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