To determine the measure of angle 1, we need to analyze the relationships between the angles formed by the transversal intersecting the parallel lines.
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Identifying angle relationships:
- If we have one angle measuring 105°, it is important to determine what relationships it has with angle 2 and angle 1.
- For two parallel lines crossed by a transversal, alternate exterior angles are equal, and corresponding angles are also equal.
- Angles on a straight line sum up to 180°; therefore, supplementary angles will also equal 180°.
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Evaluating the options:
- If angle 2 is said to be corresponding to the 105° angle, it must also measure 105°.
- If angle 1 is supplementary to angle 2, we can find angle 1 by subtracting the measure of angle 2 from 180°: \[ \text{Angle 1} = 180° - \text{Angle 2} = 180° - 105° = 75° \]
Now reviewing the provided statements:
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First option:
- Claims 105° and angle 2 are alternate exterior angles, which is incorrect (they are actually corresponding angles), but concludes correctly about angle 1 being 75°. However, the initial premise is flawed.
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Second option:
- Claims 105° and angle 2 are corresponding angles, which is correct. It concludes that angle 1 must measure 75°, which is accurate and demonstrates a correct logical flow.
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Third option:
- Claims 105° and angle 2 are alternate exterior angles, incorrectly. The conclusion about angle 1 being 105° is also incorrect.
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Fourth option:
- Claims 105° and angle 2 are corresponding angles, which is correct, but it states angle 2 measures 75° incorrectly.
The correct option is: The 105° angle and angle 2 are corresponding angles so angle 2 must measure 105°. Angles 1 and 2 are supplementary angles so angle 1 must measure 75°.
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