Question

Two angles are supplementary and their measures have a ratio of 1:3 what are the measures of the angles

Answer 1

Since the two angles are supplementary, and has a ratio of 1:3, we can say algebraically that

$x+3x=180\degree$

Let x be the measure of angle with a ratio of 1

3x be the measure of angle with a ratio of 3

Solve and we get

$\begin{gathered} x+3x=180\degree \\ 4x=180\degree \\ \frac{4x}{4}=\frac{180\degree}{4} \\ x=45\degree \end{gathered}$

Therefore, we have the following

x = 45° (measure of the first angle)

3x = 3(45°) = 135° (measure of the second angle)