Question

An angle measures 82 degrees more than the measure of its supplementary angle. What is the measure of each angle

Answer 1

Smaller Angle: 49 degrees

Bigger Angle: 131 degrees

Note that supplementary angles add up to be 180 degrees. Knowing this and the information provided in the question, we can use the following system of equations:

x + y = 180 (showing they both add up to 180)

x + 82 = y  (to show one angle is 82 more than the other)

We can use the substitution method to solve. Since the second equation ends in  "= y" we can substitute the value of it into y for the first equation.

x + y = 180; x + 82 = y  ==> x + (x + 82) = 180

And now, solve for x:

x + (x + 82) = 180

x + x + 82 = 180 > combine like terms

2x + 82 = 180

2x = 98

x = 49

So now we have the value for one of the angles! Remembering that the other angle is 82 degrees bigger, dd 49 + 82, which equals 131.

So, our two angle values are 131 and 49! This is correct since both angle measures add up to be 180, which also makes them supplementary!