Question

(d) problem 22: (first taught in lesson 16) two angles are supplementary. the measure of one angle is 5 greater than 40% of the other. find the measures of both angles. after you enter your answer press go. and go

Explanation:

Step1: Set up variables

Let one angle be \( x \). Then the other angle is \( 0.4x + 5 \).
Since supplementary angles sum to \( 180^{\circ} \), we have the equation \( x+(0.4x + 5)=180 \).

Step2: Simplify the equation

Combine like - terms: \( x+0.4x+5 = 180 \), which becomes \( 1.4x+5 = 180 \).
Subtract 5 from both sides: \( 1.4x=180 - 5=175 \).

Step3: Solve for \( x \)

Divide both sides by \( 1.4 \): \( x=\frac{175}{1.4}=125 \).

Step4: Find the other angle

Substitute \( x = 125 \) into \( 0.4x + 5 \).
\( 0.4\times125+5=50 + 5=55 \).

Answer:

\( 125 \) and \( 55 \)