Find the value of x, y, and z and show all your work.

Step-by-step explanation:

Look at the top triangle.  

It is an isosceles triangle because two of the sides are marked equal.  

The angles opposite the congruent sides are called base angles. (in the case x and z)

Base angles of an isosceles triangle are equal.

In addition, we use the Triangle angle sum theorem - the sum of the angles in a triangle is 180 degrees

60 + x + y = 180

x+z =120

but x = z so by substitution

x +x = 120

2x = 120

x = 60

z = 60

likewise for the bottom triangle:

50 +50 + Y = 180

Y = 80

3

step-by-step explanation: