Find the value of x y and z below !

Question

asked Sep 1, 2023 15.3k views

1 Answer

Tatyana Molchanova · Answer 1 · 2023-09-04T22:30:45+0000

Answer:

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 :(