the sum of the four angle measures of any convex quadrilateral is 360 degrees. if a certain convex quadrilater has angle measures of 60, 2y-10, and 10y+5 degrees, what is an expression for the degrees measure of the fourth angle?
Ø + 60 + 2y-10 + 10y + 5 = 360
Ø = 305 - 12y
To find the expression for the degree measure of the fourth angle, we can use the fact that the sum of the four angle measures of any convex quadrilateral is always 360 degrees.
Let's denote the fourth angle as "x" degrees. We already have three angles given: 60 degrees, 2y-10 degrees, and 10y+5 degrees. So, the expression becomes:
60 + (2y-10) + (10y+5) + x = 360
Simplifying the equation, we get:
2y + 10y + 60 - 10 + 5 + x = 360
Combine like terms on the left side:
12y + 55 + x = 360
Now, let's isolate "x" by moving the other terms to the right side:
x = 360 - 12y - 55
Hence, the expression for the degree measure of the fourth angle is 360 - 12y - 55.