Question

Find the value of x y and z below !

Answer 1

`x=67, y=121, z=65`

Explanation:

One property of parallelogram is that opposite angles have the same measure, so we can write down:

`(y-9)=112\\y=121`

Another property is that two adjacent angles are supplementary (meaning that they add up to 180 degrees). Thus, the following equations are true:

`(z+3)+112=180\\(x+1)+112=180`

Solve the equations:

`(z+3)+112=180\\z+115=180\\z=65\\(x+1)+112=180\\x+113=180\\x=67`

To check, add up all 4 angles and check if they sum up to 360 degrees:

`x=67, y=121, z=65\\(y-9)+(x+1)+(z+3)+112=360\\(121-9)+(67+1)+(65+3)+112=360\\112+68+68+112=360\\360=360`

And please ignore the fact that I cannot insert the degree sign :(