Question

Given the figure, find the values of x and z.

Answer 1

`\\ \sf\bull\dashrightarrow 9x-67+6x-23=180`

`\\ \sf\bull\dashrightarrow 9x+6x-67-23=180`

`\\ \sf\bull\dashrightarrow 15x-90=180`

`\\ \sf\bull\dashrightarrow 15x=180+90=270`

`\\ \sf\bull\dashrightarrow x=18`

Now

`\\ \sf\bull\dashrightarrow z=6x-23`

`\\ \sf\bull\dashrightarrow z=18(6)-23`

`\\ \sf\bull\dashrightarrow z=108-23`

`\\ \sf\bull\dashrightarrow z=85`

Answer 2

The angle with (6x-23) and (9x-67) together make a straight line, so their sum is 180:

(6x-23) + (9x-67) = 180

So you need to solve that for x.

For z, z and (6x-23) are vertical angles, so their angle measures are the same.

z = 6x-23