The sum of the four angle measures of any convex quadrilateral is

360 degrees. Suppose that a convex quadrilateral has angle measures of
90, 10y+4, and 3y-2 degrees. Write an expression for the degree measure of the fourth angle.

let the fourth angle be x°

x = 360 - (90 + 10y+4 + 3y-2)

Thank you!

To find the degree measure of the fourth angle of the quadrilateral, we can use the fact that the sum of the four angle measures in any convex quadrilateral is 360 degrees.

Let's start by writing the equation to find the sum of the three given angle measures:

90 + (10y + 4) + (3y - 2) + x = 360

Here, x represents the degree measure of the fourth angle.

Now, let's simplify the equation by combining like terms:

90 + 10y + 4 + 3y - 2 + x = 360

Combine the constants: 90 + 4 - 2 = 92

Combine the y terms: 10y + 3y = 13y

The simplified equation becomes:

92 + 13y + x = 360

To find the expression for the degree measure of the fourth angle, we isolate the x term by subtracting 92 and 13y from both sides of the equation:

92 + 13y + x - 92 - 13y = 360 - 92 - 13y

Simplify: x = 268 - 13y

Therefore, the expression for the degree measure of the fourth angle is 268 - 13y.