Question

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

Answer 1

Start by finding x.

All triangles have the property that their angles add up to 180°.

So you know from the diagram that:
36 + 63 + x = 180
Solve for x.

Similarly, looking at the larger triangle that holds the two smaller triangles, try solving for y. The top of the triangle is made up of 13° and 36°. 13 + 36 = 49.
So since we know the angles have to add up to 180°, we can solve for y in the equation:
63 + 49 + y = 180
Solve for y.

Lastly, solve for z using the same process! If you have any questions, just comment here. You've got this!

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 $68\°$