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
Great job!
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
Excellent!
The measure of angle b is 53°. You want to find the measure of angle f. You know the measure of angle b, so let's start by using the first equation to find the measure of angle a. Solve on paper. Then, enter your answer on Zearn.
dºcºb = 53ºaºfºeº

Answer 1

Let's break this down step by step:

1. Complementary Angles: Angle \( a \) and angle \( b \) are complementary, which means: \[ a + b = 90^\circ \] Since the measure of angle \( b \) is given as \( 53^\circ \), we can substitute this value into the equation to find angle \( a \): \[ a + 53 = 90 \] To solve for \( a \), we subtract \( 53 \) from both sides: \[ a = 90 - 53 = 37^\circ \]

2. Supplementary Angles: Angle \( a \) and angle \( f \) are supplementary, meaning: \[ a + f = 180^\circ \] We can now substitute the value we found for angle \( a \): \[ 37 + f = 180 \] To solve for \( f \), subtract \( 37 \) from both sides: \[ f = 180 - 37 = 143^\circ \]

So, the measure of angle \( f \) is \( 143^\circ \).