In geometry, if the angles have the same values of sine and cosine, it implies that the angles are complementary which further means that the sum of their measures should be 90°. With the given expressions for the angles above,
(x + 11) + (2x + 22) = 90
Simplifying,
3x + 33 = 90
Further simplification,
3x = 90 - 33 = 57
The value of x from the equation is 19.
Answer: x = 19