Question
How to find the measure of an angle when given the measures of its adjacent angle and the angle that contains them?
Answers
GPT-4o mini
To find the measure of an angle when you are given the measures of its adjacent angle and the angle that contains them, you can use the properties of angles.
1. **Identify the Angles**: Let's label the angles for clarity:
- Let angle A be the angle you want to find.
- Let angle B be the adjacent angle with a known measure.
- Let angle C be the angle that contains both A and B (which is often the angle formed by two rays or lines).
2. **Set Up the Relationship**: The relationship between the angles will depend on how they are positioned relative to each other:
- If angles A and B are adjacent and form angle C, then their measures can be related as follows:
\[
A + B = C
\]
- If angles A and B are supplementary angles, meaning they add up to form a straight line (180 degrees), then:
\[
A + B = 180^\circ
\]
- If angles A and B are complementary angles, meaning they add up to form a right angle (90 degrees):
\[
A + B = 90^\circ
\]
3. **Solve for Angle A**:
- Rearrange the equation based on the relationship:
\[
A = C - B \quad \text{(if A and B form angle C)}
\]
or
\[
A = 180^\circ - B \quad \text{(if A and B are supplementary)}
\]
or
\[
A = 90^\circ - B \quad \text{(if A and B are complementary)}
\]
4. **Substitute the Known Values**: Substitute the known measures of angle B and angle C (if applicable) into the equation to find the measure of angle A.
**Example**:
- Given that angle B measures 50 degrees and you know that A and B are supplementary:
\[
A + 50^\circ = 180^\circ \\
A = 180^\circ - 50^\circ = 130^\circ
\]
This method will allow you to find the measure of the angle you are looking for based on the information provided about the adjacent angle and the containing angle.
1. **Identify the Angles**: Let's label the angles for clarity:
- Let angle A be the angle you want to find.
- Let angle B be the adjacent angle with a known measure.
- Let angle C be the angle that contains both A and B (which is often the angle formed by two rays or lines).
2. **Set Up the Relationship**: The relationship between the angles will depend on how they are positioned relative to each other:
- If angles A and B are adjacent and form angle C, then their measures can be related as follows:
\[
A + B = C
\]
- If angles A and B are supplementary angles, meaning they add up to form a straight line (180 degrees), then:
\[
A + B = 180^\circ
\]
- If angles A and B are complementary angles, meaning they add up to form a right angle (90 degrees):
\[
A + B = 90^\circ
\]
3. **Solve for Angle A**:
- Rearrange the equation based on the relationship:
\[
A = C - B \quad \text{(if A and B form angle C)}
\]
or
\[
A = 180^\circ - B \quad \text{(if A and B are supplementary)}
\]
or
\[
A = 90^\circ - B \quad \text{(if A and B are complementary)}
\]
4. **Substitute the Known Values**: Substitute the known measures of angle B and angle C (if applicable) into the equation to find the measure of angle A.
**Example**:
- Given that angle B measures 50 degrees and you know that A and B are supplementary:
\[
A + 50^\circ = 180^\circ \\
A = 180^\circ - 50^\circ = 130^\circ
\]
This method will allow you to find the measure of the angle you are looking for based on the information provided about the adjacent angle and the containing angle.