Question
Which correctly describes how to determine the measure of angle 1?
2 parallel lines are crossed by a transversal to form 8 angles. Clockwise from top left, the angles are 1, 2, blank, blank; blank 81 degrees, blank, blank.
The 81° angle and angle 2 are corresponding angles so angle 2 must measure 81°. Angles 1 and 2 are supplementary angles so angle 1 must measure 99°.
The 81° angle and angle 2 are alternate interior angles so angle 2 must measure 81°. Angles 1 and 2 are supplementary angles so angle 1 must measure 99°.
The 81° angle and angle 2 are corresponding angles so angle 2 must measure 99°. Angles 1 and 2 are supplementary angles so angle 1 must measure 81°.
The 81° angle and angle 2 are alternate interior angles so angle 2 must measure 99°. Angles 1 and 2 are supplementary angles so angle 1 must measure 81°.
2 parallel lines are crossed by a transversal to form 8 angles. Clockwise from top left, the angles are 1, 2, blank, blank; blank 81 degrees, blank, blank.
The 81° angle and angle 2 are corresponding angles so angle 2 must measure 81°. Angles 1 and 2 are supplementary angles so angle 1 must measure 99°.
The 81° angle and angle 2 are alternate interior angles so angle 2 must measure 81°. Angles 1 and 2 are supplementary angles so angle 1 must measure 99°.
The 81° angle and angle 2 are corresponding angles so angle 2 must measure 99°. Angles 1 and 2 are supplementary angles so angle 1 must measure 81°.
The 81° angle and angle 2 are alternate interior angles so angle 2 must measure 99°. Angles 1 and 2 are supplementary angles so angle 1 must measure 81°.
Answers
GPT-4o mini
To determine the measure of angle 1 based on the description provided, let's analyze the given options.
1. If the 81° angle is corresponding to angle 2:
- This implies that angle 2 must also be 81°.
- Since angles 1 and 2 are supplementary (the sum of their measures is 180°), angle 1 must measure 99° (180° - 81° = 99°).
2. If the 81° angle is alternate interior to angle 2:
- In this case, angle 2 must still be 81°, for the same reasoning as above.
- Therefore, angle 1 would likewise measure 99°.
Now reviewing the provided statements:
1. The first option correctly states that angle 2 must measure 81°, and angle 1 would then measure 99°, which aligns with the reasoning above.
2. The second option also recognizes angle 2 as 81° (correctly being alternate interior) and concludes angle 1 must be 99° as well, which is accurate.
3. The third option mistakenly states that angle 2 must measure 99° which is incorrect if angle 2 is corresponding to the 81° angle.
4. The fourth option incorrectly concludes that angle 2 is 99° as well, leading angle 1 to be incorrectly assessed to be 81°.
Based on this analysis, both the first and second options are correct in identifying angles. Therefore, the determinations for angle 1 measuring 99° are consistent in those options.
**Conclusion:** The correct statements about how to determine angle 1 are:
1. The 81° angle and angle 2 are corresponding angles so angle 2 must measure 81°. Angles 1 and 2 are supplementary angles so angle 1 must measure 99°.
2. The 81° angle and angle 2 are alternate interior angles so angle 2 must measure 81°. Angles 1 and 2 are supplementary angles so angle 1 must measure 99°.
Both of these approaches correctly lead to angle 1 measuring 99°.
1. If the 81° angle is corresponding to angle 2:
- This implies that angle 2 must also be 81°.
- Since angles 1 and 2 are supplementary (the sum of their measures is 180°), angle 1 must measure 99° (180° - 81° = 99°).
2. If the 81° angle is alternate interior to angle 2:
- In this case, angle 2 must still be 81°, for the same reasoning as above.
- Therefore, angle 1 would likewise measure 99°.
Now reviewing the provided statements:
1. The first option correctly states that angle 2 must measure 81°, and angle 1 would then measure 99°, which aligns with the reasoning above.
2. The second option also recognizes angle 2 as 81° (correctly being alternate interior) and concludes angle 1 must be 99° as well, which is accurate.
3. The third option mistakenly states that angle 2 must measure 99° which is incorrect if angle 2 is corresponding to the 81° angle.
4. The fourth option incorrectly concludes that angle 2 is 99° as well, leading angle 1 to be incorrectly assessed to be 81°.
Based on this analysis, both the first and second options are correct in identifying angles. Therefore, the determinations for angle 1 measuring 99° are consistent in those options.
**Conclusion:** The correct statements about how to determine angle 1 are:
1. The 81° angle and angle 2 are corresponding angles so angle 2 must measure 81°. Angles 1 and 2 are supplementary angles so angle 1 must measure 99°.
2. The 81° angle and angle 2 are alternate interior angles so angle 2 must measure 81°. Angles 1 and 2 are supplementary angles so angle 1 must measure 99°.
Both of these approaches correctly lead to angle 1 measuring 99°.