In the diagram shown, m3 = 3x - 16 and m4 = x + 84.

Find the value of x.

Given that the m3 and m4 are both supplementary angles, we can therefore conclude that when we sum them up we get 180. Because supplemantary angles add up to 180.

Thus;

m3+m4=180

(3x-16) + (x+84) = 180

opening the brackets we get:

3x-16+x+84=180

3x-x-16+84=180

2x+68=180

2x=180-64

2x=112

thus;

x=112/2

x=56

The answer is x=56