Question
The measure of angle1 is 39degrees. Find the measure of the angle adjacent to angle1. The figure is not drawn to scale. Use pencil and paper. Explain how you know your answer is reasonable.
1
Question content area bottom
Part 1
The measure of the angle adjacent to angle1 is
enter your response here degrees.
1
Question content area bottom
Part 1
The measure of the angle adjacent to angle1 is
enter your response here degrees.
Answers
GPT-4o mini
In the context of angles, "adjacent" typically refers to two angles that share a common vertex and a common side, but do not overlap. The measure of the adjacent angle depends on the relationship between the two angles.
If we assume that angle 1 (which measures 39 degrees) is part of a linear pair with the adjacent angle (meaning they form a straight line), then we can use the fact that the sum of angles on a straight line is always 180 degrees.
To find the measure of the adjacent angle:
\[
\text{Measure of adjacent angle} = 180^\circ - \text{Measure of angle 1}
\]
Substituting the measure of angle 1:
\[
\text{Measure of adjacent angle} = 180^\circ - 39^\circ = 141^\circ
\]
So, the measure of the angle adjacent to angle 1 is 141 degrees.
### Reasonableness Check:
1. **Sum of Angles**: Since angle 1 is 39 degrees and the adjacent angle is calculated to be 141 degrees, their sum is:
\[
39^\circ + 141^\circ = 180^\circ
\]
This confirms that they are supplementary angles, as they should be on a straight line.
2. **Magnitude**: The adjacent angle measuring 141 degrees is consistent with our expectations. It is larger than 90 degrees, which is reasonable given that angle 1 is only 39 degrees.
Therefore, the measure of the angle adjacent to angle 1 is **141 degrees**.
If we assume that angle 1 (which measures 39 degrees) is part of a linear pair with the adjacent angle (meaning they form a straight line), then we can use the fact that the sum of angles on a straight line is always 180 degrees.
To find the measure of the adjacent angle:
\[
\text{Measure of adjacent angle} = 180^\circ - \text{Measure of angle 1}
\]
Substituting the measure of angle 1:
\[
\text{Measure of adjacent angle} = 180^\circ - 39^\circ = 141^\circ
\]
So, the measure of the angle adjacent to angle 1 is 141 degrees.
### Reasonableness Check:
1. **Sum of Angles**: Since angle 1 is 39 degrees and the adjacent angle is calculated to be 141 degrees, their sum is:
\[
39^\circ + 141^\circ = 180^\circ
\]
This confirms that they are supplementary angles, as they should be on a straight line.
2. **Magnitude**: The adjacent angle measuring 141 degrees is consistent with our expectations. It is larger than 90 degrees, which is reasonable given that angle 1 is only 39 degrees.
Therefore, the measure of the angle adjacent to angle 1 is **141 degrees**.