Question

What are the measurements of x and y

Answer 1

Firstly we know that a straight line is 180°

So lets find each angle then
90 + 12 + 15 + x + x + x = 180
117 + 3x = 180
-117          -117
3x = 63
$\frac{3x}{3} = \frac{63}{3}$
x = 21°

Same thing for the angle y
90 + 15 + 12 + y + y = 180
117 + 2y = 180
-117          -117
2y = 63
$\frac{2y}{2} = \frac{63}{2}$
y = 31.5°

The whole is 360°
check: 
31.5 + 31.5 + 15 + 15 + 12 + 12 + 90 + 90 + 21 + 21 + 21 = 360
360 = 360

Answer 2

X=21°
y=31.5°

Explanation:
Since it is a whole circle (360°) and there are 40 section (90° each).
2 of the 90° +(180°)are clearly stated there so you do:
360°-180°=180°

1. On the side that have 2 'y's you do:
90°-(12+15)=63
Then 63/2=31.5°
Therefore y=31.5°

2. On the side with 3 'x's you do:
90°-(12+15)=63
Then 63/3=21°
Therefore x=21°

To cross check you do:
90+90+15+12+21+21+21+15+12+31.5+31.5=360

I hope you find this helpful.