Question
Which statement is true about the angles below?
(1 point)
Responses
If angle 1 is 110°
, then angle 3 is also 110°
because they are adjacent angles.
If angle 1 is 110 degrees, then angle 3 is also 110 degrees because they are adjacent angles.
If angle 1 is 110°
, then angle 3 is also 110°
because they are vertical angles.
If angle 1 is 110 degrees, then angle 3 is also 110 degrees because they are vertical angles.
If angle 1 is 110°
, then angle 3 is 70°
because they are complementary angles.
If angle 1 is 110 degrees, then angle 3 is 70 degrees because they are complementary angles.
If angle 1 is 110°
, then angle 3 is 70°
because they are supplementary angles.
(1 point)
Responses
If angle 1 is 110°
, then angle 3 is also 110°
because they are adjacent angles.
If angle 1 is 110 degrees, then angle 3 is also 110 degrees because they are adjacent angles.
If angle 1 is 110°
, then angle 3 is also 110°
because they are vertical angles.
If angle 1 is 110 degrees, then angle 3 is also 110 degrees because they are vertical angles.
If angle 1 is 110°
, then angle 3 is 70°
because they are complementary angles.
If angle 1 is 110 degrees, then angle 3 is 70 degrees because they are complementary angles.
If angle 1 is 110°
, then angle 3 is 70°
because they are supplementary angles.
Answers
GPT-4o mini
To determine which statement is true about the angles based on the relationships provided, we need to understand the definitions of adjacent, vertical, complementary, and supplementary angles:
1. **Adjacent Angles**: Two angles that share a common side and a common vertex but do not overlap. This does not necessarily mean they are equal in measure.
2. **Vertical Angles**: Angles that are opposite each other when two lines intersect. Vertical angles are always equal.
3. **Complementary Angles**: Two angles whose measures add up to 90 degrees.
4. **Supplementary Angles**: Two angles whose measures add up to 180 degrees.
Given that angle 1 is 110°, we can analyze each statement:
- **Statement about Adjacent Angles**: This is false because adjacent angles do not have to be equal in measure.
- **Statement about Vertical Angles**: This is true only if angle 3 is the vertical angle to angle 1, but we don't have that confirmation. We cannot declare it true without knowing the specific configuration of the angles.
- **Statement about Complementary Angles**: This is false because 110° + angle 3 cannot equal 90°.
- **Statement about Supplementary Angles**: This is true, as 110° + 70° = 180°. So, if angle 3 is supplementary to angle 1, it would be 70°.
Thus, the true statement based on the provided options is:
**If angle 1 is 110°, then angle 3 is 70° because they are supplementary angles.**
1. **Adjacent Angles**: Two angles that share a common side and a common vertex but do not overlap. This does not necessarily mean they are equal in measure.
2. **Vertical Angles**: Angles that are opposite each other when two lines intersect. Vertical angles are always equal.
3. **Complementary Angles**: Two angles whose measures add up to 90 degrees.
4. **Supplementary Angles**: Two angles whose measures add up to 180 degrees.
Given that angle 1 is 110°, we can analyze each statement:
- **Statement about Adjacent Angles**: This is false because adjacent angles do not have to be equal in measure.
- **Statement about Vertical Angles**: This is true only if angle 3 is the vertical angle to angle 1, but we don't have that confirmation. We cannot declare it true without knowing the specific configuration of the angles.
- **Statement about Complementary Angles**: This is false because 110° + angle 3 cannot equal 90°.
- **Statement about Supplementary Angles**: This is true, as 110° + 70° = 180°. So, if angle 3 is supplementary to angle 1, it would be 70°.
Thus, the true statement based on the provided options is:
**If angle 1 is 110°, then angle 3 is 70° because they are supplementary angles.**