Use the relationships between angle pairs to find the measure of angle f.

Question

Angle a and angle b are complementary angles. Write an equation to represent the relationship between angle a and angle b.
dºcºbºaºfºeº
You got it!
Angle a and angle f are supplementary angles. Write an equation to represent the relationship between angle a and angle f.
a+b=90
dºcºbºaºfºeº

Answer 1

To find the measure of angle \( f \), we can use the relationships you provided.

1. Since angles \( a \) and \( b \) are complementary, we have the equation: \[ a + b = 90^\circ \]

2. Since angles \( a \) and \( f \) are supplementary, we have the equation: \[ a + f = 180^\circ \]

Now we can express \( f \) in terms of \( a \) using the second equation. Rearranging \( a + f = 180^\circ \) gives: \[ f = 180^\circ - a \]

Substituting for \( a \):

From \( a + b = 90^\circ \), we can express \( b \) in terms of \( a \): \[ b = 90^\circ - a \]

If needed, you can also substitute this expression for \( b \) back into another equation, but for the purpose of finding the angle \( f \), using \( f = 180^\circ - a \) is sufficient.

Summary of Relationships:

• \( a + b = 90^\circ \) (Complementary)
• \( a + f = 180^\circ \) (Supplementary)

You can now find the specific measures of angles \( a \), \( b \), and \( f \) if you have numeric values or additional equations involving these angles.