Solve for x
find the measure of angle y
(EXPLAIN YOUR ANSWER AND HOW YOU GOT THE ANSWER)

x=16°, y= 120°

Step-by-step explanation:

Information needed

All angles in the diagram will  to 360° equal

The empty angle is (x+8) because of the vertical angles property

Solve for x:

(5x-14)+(x+8)= 90° because it's given that the angle below is a right angle (90°)

(5x-14)+(x+8)= 90°

5x-14+x+8= 90°

5x+x-14+8= 90°

6x-6= 90°

  +6    +6

6x= 96°

/6    /6

x= 16°

Solve for y:

x= 16°

90+(5x-14)+(x+8)+(x+8)

90+66+24+24

= 204°

360°-204°= 120°

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47