The angles in a triangle are represented by 5x, 8x, and 2x+9. what is the value of x?

x = 11.4

Step-by-step explanation:

The sum of the angles of any triangle must add up to 180°.  Since we have the expressions for each angle:  5x, 8x, and (2x +9), we can solve for the variable of 'x' by adding the expressions together and setting them equal to 180:

5x + 8x + (2x +9) = 180

Combine like terms:  15x + 9 = 180

Use inverse operations: 15x + 9 - 9 = 180 - 9

                                                     15x = 171  or x = 11.4

Check:  5(11.4) + 8(11.4) + 2(11.4) + 9 = 57 + 91.2 + 22.8 + 9 = 180