Question

Given the figure below, find the values of x and z.x(5x + 8)(8x - 23)

Answer 1

Two angles that fall on a line (side-by-side) add up to 180 degrees.

From the figure, we can write:

`(8x-23)+(5x+8)=180`

Now we can do a little algebra and solve for x:

`\begin{gathered} (8x-23)+(5x+8)=180 \\ 13x-23+8=180 \\ 13x-15=180 \\ 13x=180+15 \\ 13x=195 \\ x=(195)/(13) \\ x=15 \end{gathered}`

Also from another pair, we can write:

`z+(5x+8)=180`

We know the value of x is "15". We plug it in and solve for z:

`\begin{gathered} z+5(15)+8=180 \\ z+75+8=180 \\ z+83=180 \\ z=180-83 \\ z=97 \end{gathered}`

Thus, we have our answer. They are:

`x=15,z=97`