Question

in this figure triangle ABC is similar to APQ. therefore, the value of x is___ and the value of y is ___.

Answer 1

Going by the diagram, you just read the value of x. The value of y requires a little bit of calculation. 

Step One
Find x
You just read the value.
x is the same as the 70 degree angle. That comes about from parallel lines.
x = 70 degrees. <<<< answer

Step Two
Find y 
All triangles have 180 degrees.
So ABC has 180 degrees.
70 + 50 + <ACB = 180         Combine like terms
120 + <ACB = 180               Subtract 120 from both sides
<ACB = 180 - 120
<ACB = 60

y = <ACB
y = 60 degrees.    <<<< Answer. 

Answer 2

Going by the diagram, you just read the value of x. The value of y requires a little bit of calculation.  

Step One

Find x

You just read the value.

x is the same as the 70 degree angle. That comes about from parallel lines.

x = 70 degrees. <<<< answer

Step Two

Find y  

All triangles have 180 degrees.

So ABC has 180 degrees.

70 + 50 + <ACB = 180         Combine like terms

120 + <ACB = 180               Subtract 120 from both sides

<ACB = 180 - 120

<ACB = 60

y = <ACB

y = 60 degrees.    <<<< Answer.