The measure of an angle is two times the measure of its supplementary angle. What is the measure of each angle?

Question

i need two measurements

Answer 1

Hi Vianca!

Let's use a system of equations to solve this. We can call one angle x and the other angle y. We know the angles are supplementary, so their sum must be 180. We also know one angle is twice the other. We can write these two facts as equations:

x + y = 180

x = 2y

(Note that it doesn't matter which angle you call x and which you call y, so your second equation could also be y = 2x.)

Now you can substitute the value of x in the second equation (2y) into the first equation and solve for y:

(2y) + y = 180

3y = 180

y = 60

Finally, substitute this value for y in either of the two original equations. Let's use the first one:

x + 60 = 180

x = 120

As a sanity check, let's use the second equation instead:

x = 2(60)

x = 120

So our two angles are 60 degrees and 120 degrees. They are supplementary agles (60 + 120 = 180) and one is two times the other (120 = 2*60).

Hope this makes sense!

Best,

Kaleab