Question
What is a step-by-step solution for finding the value of angle a when angle b is given for supplementary angles?
Answers
GPT-4o mini
To find the value of angle \( a \) when angle \( b \) is given for supplementary angles, you can follow these step-by-step instructions. Supplementary angles are two angles whose measures add up to \( 180^\circ \).
### Step 1: Understand the Relationship
Know that if two angles are supplementary, the sum of their measures can be expressed with the equation:
\[
a + b = 180^\circ
\]
### Step 2: Identify the Given Angle
Let's say you are given the measure of angle \( b \). For example, suppose \( b = 70^\circ \).
### Step 3: Substitute the Value into the Equation
Plug the value of angle \( b \) into the equation:
\[
a + 70^\circ = 180^\circ
\]
### Step 4: Isolate Angle \( a \)
To find angle \( a \), subtract \( b \) from \( 180^\circ \):
\[
a = 180^\circ - b
\]
### Step 5: Perform the Calculation
Now, substitute the value of \( b \) into this equation:
\[
a = 180^\circ - 70^\circ
\]
### Step 6: Final Calculation
Calculate \( a \):
\[
a = 110^\circ
\]
### Conclusion
Thus, if angle \( b \) is \( 70^\circ \), then angle \( a \) is \( 110^\circ \). You can use this method with any value of \( b \) to find the corresponding angle \( a \). Just remember to subtract the given angle \( b \) from \( 180^\circ \).
### Step 1: Understand the Relationship
Know that if two angles are supplementary, the sum of their measures can be expressed with the equation:
\[
a + b = 180^\circ
\]
### Step 2: Identify the Given Angle
Let's say you are given the measure of angle \( b \). For example, suppose \( b = 70^\circ \).
### Step 3: Substitute the Value into the Equation
Plug the value of angle \( b \) into the equation:
\[
a + 70^\circ = 180^\circ
\]
### Step 4: Isolate Angle \( a \)
To find angle \( a \), subtract \( b \) from \( 180^\circ \):
\[
a = 180^\circ - b
\]
### Step 5: Perform the Calculation
Now, substitute the value of \( b \) into this equation:
\[
a = 180^\circ - 70^\circ
\]
### Step 6: Final Calculation
Calculate \( a \):
\[
a = 110^\circ
\]
### Conclusion
Thus, if angle \( b \) is \( 70^\circ \), then angle \( a \) is \( 110^\circ \). You can use this method with any value of \( b \) to find the corresponding angle \( a \). Just remember to subtract the given angle \( b \) from \( 180^\circ \).