Let's analyze the information provided and evaluate each statement based on the properties of angles in parallel lines cut by transversals.
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m∠A = 20°:
- Since angles A and B form a straight line, this means they are supplementary. If angle B is 60 degrees, then: \[ m∠A + m∠B = 180° \] \[ m∠A + 60° = 180° \] \[ m∠A = 120° \]
- This statement is false.
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∠B and the angle marked 60° are alternate exterior angles:
- Alternate exterior angles are formed on opposite sides of a transversal and outside the parallel lines. If angle B is 60 degrees and there is another angle marked 60 degrees on the opposite side of the transversal, they can be considered alternate exterior angles. If this is accurately describing the given angles, this statement is true.
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m∠C = 100° because it is a vertical angle to the angle marked 100°:
- Since angle C is stated to be a vertical angle to the angle marked 100°, it must also measure 100°. Therefore, this statement is true.
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∠B and ∠C are supplementary angles:
- For angles B (60°) and C (100°): \[ m∠B + m∠C = 60° + 100° = 160° \]
- Since supplementary angles must add up to 180°, this statement is false.
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m∠A + m∠B + m∠C = 180°:
- Now we can check this equation with our earlier findings: \[ m∠A = 120°, ; m∠B = 60°, ; m∠C = 100° \] \[ 120° + 60° + 100° = 280° \]
- This also does not equal 180°, thus the statement is false.
The true statements are:
- ∠B and the angle marked 60° are alternate exterior angles.
- m∠C = 100° because it is a vertical angle to the angle marked 100°.
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