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Question

The sum of the four angle measures of any convex quadrilateral is 360 degrees. Suppose that a convex quadrilateral has angle measures of 60, 9y+10, and 8y-5 degrees. Write an expression for the degree measure of the fourth angle.

Answer 1

Quadrilateral has 4 sides.

The sum of the internal angles of an n-sided polygon is 

 

     180(n-2) 

  = 180(4-2)

  = 180(2)

  = 360

 

We have values and expressions for 3 of the 4 angles.

So we would subtract the sum of the 3 given angles from 360, to find the 4th angle.

 

    the 4th angle = 360 - (60 + 9y+10 + 8y - 5)

                          = 360 - (60 + 10 - 5 + 9y + 8y)

                          = 360 - (65 + 17y)

                          = 360 - 65 -17y

                          = -17y + 295