The measures of two supplementary angles are in the ratio 5:1. What is the measure of the smaller triangle?

A/B = 5
A + B = 180

Solve those 2 equations in two unknowns.
B is the smaller angle.

Hint: substitute 5B for A in the second equation. Then only B is in the equation, and you can solve for it.

To find the measure of the smaller angle, we can set up a system of equations based on the given ratio and the fact that supplementary angles add up to 180 degrees.

Let's assume that the measure of the smaller angle is B degrees. We can then express the measure of the larger angle as 5B degrees since the ratio is given as 5:1.

We can set up the following equations based on the information given:
Equation 1: A/B = 5 (where A represents the measure of the larger angle)
Equation 2: A + B = 180 (since the angles are supplementary and add up to 180 degrees)

To solve this system of equations, we will substitute 5B for A in Equation 2, as suggested:
5B + B = 180

Combining like terms:
6B = 180

To solve for B, divide both sides of the equation by 6:
B = 180 / 6
B = 30

Therefore, the measure of the smaller angle is 30 degrees.