Question

Find the values of x, y, and z. The diagram is not to scale.

Answer 1

x=81 y=81 z =68

Explanation:

Answer 2

we know that

The sum of the internal angles in the triangle must be
`180` degrees

see the attached figure with letters to better understand the problem

Step
`1`

Find the measure of the angle x

In the triangle ABC

`63\°+36\°+x\°=180\°`

solve for x

`99\°+x\°=180\°`

`x\°=180\°-99\°`

`x=81\°`

therefore

the answer Part a) is

the measure of angle x is
`81\°`

Step
`2`

Find the measure of the angle z

we know that

`x+z=180\°` --------> by supplementary angles

substitute the value of x

`81\°+z=180\°`

`z=180\°-81\°`

`z=99\°`

therefore

the answer Part b) is

the measure of angle z is
`99\°`

Step
`3`

Find the measure of the angle y

In the triangle ACD

`13\°+z\°+y\°=180\°`

solve for y

`13\°+99\°+y\°=180\°`

`112\°+y\°=180\°`

`y\°=180\°-112\°`

`y\°=68\°`

therefore

the answer Part c) is

the measure of angle y is
`68\°`