The value of the angles
∠ E = 36 degrees
∠ D = ∠ F = 72 degrees
How to find the angles
According to the information provided
Let the number be x
The measure of ∠ Dis nine more than nine times a number.
The measure of ∠F is twelve less than twelve times the number.
This give rise to the equation
9 + 9x = 12x - 12
9 + 12 = 12x - 9x
21 = 3x
x = 7
∠ D = 9 + 9x = 9 + 9 * 7 = 72
Sum of the angles in a triangle
∠ D + ∠ E + ∠ F = 180
72 + 72 + ∠ E = 180
∠ E = 180 - 72 - 72
∠ E = 36