Question
What type of angles are shown? In the explain box - Find the measure of angle "b"
In the explain box. Write the measure of angle b.
adjancet
supplementary
vertical
complementary
Explain your thinking.
In the explain box. Write the measure of angle b.
adjancet
supplementary
vertical
complementary
Explain your thinking.
Answers
GPT-4o mini
To determine the measure of angle "b," we first need to understand the relationships between the different types of angles mentioned: adjacent, supplementary, vertical, and complementary.
1. **Adjacent Angles**: These are angles that share a common side and a common vertex but do not overlap.
2. **Supplementary Angles**: Two angles are supplementary if the sum of their measures is 180 degrees.
3. **Vertical Angles**: When two lines intersect, the angles opposite each other are vertical angles. They are always congruent, meaning they have the same measure.
4. **Complementary Angles**: Two angles are complementary if the sum of their measures is 90 degrees.
If we have information about other angles or the relationships between angle "b" and one or more of these angles, we can start calculating its measure.
### Find the Measure of Angle "b"
1. Identify if angle "b" is adjacent, supplementary, vertical, or complementary to any given angle in the problem.
2. If "b" is supplementary to an angle measure \(A\), we can find \(b\) using the formula:
\[
b = 180^\circ - A
\]
3. If "b" is complementary to an angle measure \(C\), we can find \(b\) using the formula:
\[
b = 90^\circ - C
\]
4. If "b" is vertical to another angle \(D\), then:
\[
b = D
\]
### Example Calculation
Assuming we have angle "b" as supplementary to a given angle of 70 degrees:
- Since they are supplementary:
\[
b = 180^\circ - 70^\circ = 110^\circ
\]
### Conclusion
In the explanation box, the measure of angle "b" would be stated as follows:
**The measure of angle b is 110 degrees.**
This conclusion holds under the assumption that angle b is supplementary to an angle of 70 degrees. Adjust according to the specific context of angles provided in the problem.
1. **Adjacent Angles**: These are angles that share a common side and a common vertex but do not overlap.
2. **Supplementary Angles**: Two angles are supplementary if the sum of their measures is 180 degrees.
3. **Vertical Angles**: When two lines intersect, the angles opposite each other are vertical angles. They are always congruent, meaning they have the same measure.
4. **Complementary Angles**: Two angles are complementary if the sum of their measures is 90 degrees.
If we have information about other angles or the relationships between angle "b" and one or more of these angles, we can start calculating its measure.
### Find the Measure of Angle "b"
1. Identify if angle "b" is adjacent, supplementary, vertical, or complementary to any given angle in the problem.
2. If "b" is supplementary to an angle measure \(A\), we can find \(b\) using the formula:
\[
b = 180^\circ - A
\]
3. If "b" is complementary to an angle measure \(C\), we can find \(b\) using the formula:
\[
b = 90^\circ - C
\]
4. If "b" is vertical to another angle \(D\), then:
\[
b = D
\]
### Example Calculation
Assuming we have angle "b" as supplementary to a given angle of 70 degrees:
- Since they are supplementary:
\[
b = 180^\circ - 70^\circ = 110^\circ
\]
### Conclusion
In the explanation box, the measure of angle "b" would be stated as follows:
**The measure of angle b is 110 degrees.**
This conclusion holds under the assumption that angle b is supplementary to an angle of 70 degrees. Adjust according to the specific context of angles provided in the problem.