If ray np bisects angle mnq and measure of angle mnq= 8x + 12 and measure of pnq= 78 degrees and measure of angle rnm= 3y -9, find the values of x and y

9514 1404 393

Step-by-step explanation:

Given:

  ∠MNP +∠PNQ = ∠MNQ = (8x+12)°

  ∠MNP = ∠PNQ = 78° = (3y-9)°

Find:

  x, y

Solution:

The overall angle measure is ...

  78° +78° = (8x +12)°

  78 = 4x +6 . . . . . . . . . divide by 2°

  72 = 4x . . . . . . . . . subtract 6

  18 = x . . . . . . . . divide by 4

__

One angle measure is ...

  78° = (3y -9)°

  26 = y -3 . . . . . . divide by 3°

  29 = y . . . . . . . . add 3

The values of x and y are 18 and 29, respectively.

Comment on the question

We have interpreted the statement "angle RNM = 3y-9" to mean "angle PNM = 3y-9". This interpretation was chosen because point R is not mentioned or described anywhere else in the problem statement.

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