Question

practice d: (first taught in lesson 16) two angles are supplementary. the measure of one angle is 6 less than 20% of the other. find the measures of both angles. after you enter your answer press go. and

Explanation:

Step1: Set up variables

Let one angle be \(x\). Then the other angle is \(0.2x - 6\).

Step2: Use the supplementary - angle property

Since supplementary angles sum to \(180^{\circ}\), we have the equation \(x+(0.2x - 6)=180\).
Simplify the left - hand side: \(x + 0.2x-6=1.2x - 6\).
So, \(1.2x-6 = 180\).
Add \(6\) to both sides: \(1.2x=180 + 6=186\).
Divide both sides by \(1.2\): \(x=\frac{186}{1.2}=155\).

Step3: Find the second angle

Substitute \(x = 155\) into \(0.2x-6\).
\(0.2\times155-6=31 - 6=25\).

Answer:

\(25\) and \(155\)