Let's call the unknown angles ∠ A and ∠ B. We know that ∠ A and ∠ B form a linear pair and, therefore, they are supplementary angles. Since the sum of measures of supplementary angles is 180^(∘), we can write an equation.
m∠ A + m∠ B = 180^(∘)
We are told that the measure of one angle is 13 the measure of the other angle. Assume that ∠ A is the smaller angle and let's call its measure x. Rather than thinking of the smaller angle as 13 of the measure of the larger angle, we can think of the larger angle as 3 times the measure of the smaller one.
m∠ A =& x
m∠ B =& 3x
Now we can substitute these values into our equation and solve for x.
