Find the values of x and y

9514 1404 393

  x = 50

  y = 33

Step-by-step explanation:

In a right triangle the acute angles are complements of each other.

  x = 90 -40

  x = 50

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An exterior angle of a triangle is equal to the sum of the remote interior angles. Here, that means ...

  71° +x° = 2y° +55°

  16 +x = 2y . . . . . . . . . . . . . subtract 55°, divide by °

  (16 +50)/2 = y = 33 . . . . . divide by 2 and substitute for x

The values of x and y are 50 and 33, respectively.