Question

Find the measures of two supplementary angles m and n if m=6x+3 and n=2x-7

Answer 1

When two angles are supplementary, their angle measures add up to 180°. That means that the angles measures of angle m and angle n should add up to 180. With this information, you can set up the equation m + n = 180. You can find the value of x by substituting m and n with their values and solving algebraically.

6x + 3 + 2x - 7 = 180       Add up like values (6x and 2x) (3 and -7)
              8x - 4 = 180       Add 4 to both sides      
                   8x = 184       Divide both sides by 8
                     x = 23

Now to find the measures of angles m and n, substitute the x value into both of the equations and solve.

m = 6x + 3              Substitute
m = 6(23) + 3         Multiply
m = 138 + 3           Add
m = 141°

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n = 2x - 7               Substitute
n = 2(23) - 7          Multiply
n = 46 - 7              Subtract
n = 39°

You can check your work by adding the two angle measures to make sure hey are supplementary.

141° + 39° = 180°

So angle m is 141° and angle n is 39°.