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°.