If an angle in standard position has its terminal side passing through the point in the first quadrant, what is the measure of angle in degrees?
Table of contents
- 0. Review of College Algebra4h 45m
- 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
1. Measuring Angles
Angles in Standard Position
Multiple Choice
If angle has a measure of , what is the measure of angle if point lies on the terminal side of angle such that , , and are collinear and is the vertex?
A
B
C
D
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Verified step by step guidance1
Identify the given angle \( \angle CBD = 140^\circ \) and note that points \( A \), \( B \), and \( D \) are collinear with \( B \) as the vertex.
Since \( A \), \( B \), and \( D \) are collinear, the angle formed by \( A \), \( B \), and \( D \) is a straight angle, which measures \( 180^\circ \).
Recognize that \( \angle CBD \) and \( \angle ABD \) share the vertex \( B \) and lie on opposite sides of the line through \( A \), \( B \), and \( D \), making them supplementary angles.
Use the supplementary angle relationship: \( \angle ABD + \angle CBD = 180^\circ \).
Solve for \( \angle ABD \) by subtracting the measure of \( \angle CBD \) from \( 180^\circ \): \( \angle ABD = 180^\circ - 140^\circ \).
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