Question

two angles are supplementary. one of them is three times the other. find the measure of the larger angle

Answer 1

Two angles are supplementary means their sum is 180 degrees.  Let the two angles be A and 3A. This also satisfies the condition that one angle is three times the other.  Now, A+3A = 180 degrees hence, 4A=180 degrees, thus, A=45 degrees Hence the larger angle of the two i.e, value of 3A is 45*3 or 135 degrees.

Answer 2

Let x be the measure of the larger angle, and y the measure of the smaller one. We know that the sum of supplementary angles is allays 180°, so x+y=180. We also know that the smaller angle is three times the larger one, so x=3y. Now we can solve the system of equations to get our answer:
$\left \{ {{x+y=180} \atop {x=3y}} \right.$
Replacing equation 2 into equation 1:
$3y+y=180$
$4y=180$
$y= \frac{180}{4}$
$y=45$
Now that we know the value of our smaller angle, we just need to replace it into equation 2 to get the measure of our larger one:
$x=(3)(45)$
$x=135$

We can conclude that the measure of the larger angle is 135°.