Question

find the measure of an angle such that the sum of the measures of its complement and its supplement is 250 degrees.

Answer 1

You can set this up as a system of equations. When I solved it I used 3 variables x,y,and z. X is the angle we are trying to find, Y is the complement and Z is the supplement.

X+Y=90 (since Y is the complement)

X+Z=180 (Z is the supplement)

Y+Z=250 (from the question)

To get Y in terms of Z subtract Z to get it on the right hand side. You end up with Y=250-Z. Now get X in terms of Z by subtracting Z from X+Z=180 leaving you with X=180-Z. Substitute both equations back into X+Y=90 which looks like this: (180-Z)+(250-Z)=90. Now simplify and solve for Z. 430-2Z=90

340=2Z

Z=170

Now plug in 170 for Z in Y+Z=250

Y+170=250

Y=80

Now we have Y=80 and Z=170 which we can plug in to either equation to solve for X.

X+80=90

X=10

X+170=180

X=10

Therefore your angle is 10 degrees.

Answer 2

Answer: 10°

Step-by-step explanation: In this problem, we are going to need to use variables to represent three different things. We will need to use variables to represent an angle, its complement, and its supplement. Now, let's represent our variables.

X ⇒ angle

90 - x ⇒ complement

180 - x ⇒ supplement

Now, we can use the second part of the problem to set up our equation. If the sum of the measures of its complement and supplement is 250°, that means we can set up our equation.

(90 - x) + (180 - x) = 250

Now, we can simplify on the left side.

270 - 2x = 250

-270 -270 ← subtract 270 on both sides

-2x = -20

-2 -2 ← divide both sides by -2

X = 10°

Therefore, our angle measures 10°.