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

we know that

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

see the attached figure with letters to better understand the problem

Step

Find the measure of the angle x

In the triangle ABC

solve for x

therefore

the answer Part a)  is

the measure of angle x is

Step

Find the measure of the angle z

we know that

--------> by supplementary angles

substitute the value of x

therefore

the answer Part b)  is

the measure of angle z is

Step

Find the measure of the angle y

In the triangle ACD

solve for y

therefore

the answer Part c)  is

the measure of angle y is

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle

The answer is 41.7 because 1.39 times 30 is 41.7