We know that sin x = cos 50°.
To solve for x, we need to find the angle whose sine is equal to cos 50°.
We can use the trigonometric identity that sin (90° - θ) = cos θ.
So, sin x = cos 50° can be rewritten as sin x = sin (90° - 50°).
Using the identity, we have:
sin x = sin 40°
Now, we need to find the angle x whose sine is equal to sin 40°.
Since sine is a periodic function, there are multiple angles whose sine is equal to a given value.
One such angle is x = 40°.
However, sine is also negative in the third and fourth quadrants.
In the third quadrant, x = 180° - 40° = 140° and in the fourth quadrant, x = 360° - 40° = 320° also satisfy the equation sin x = sin 40°.
However, since x has to be between 0° and 360°, we can eliminate the30°.
Therefore, the possible values of x are 40°, 140°, and 320°.
However, since we know that sin x = cos 50° and cos is positive in the first quadrant, x cannot be in the third or fourth quadrants.
Therefore, the only possible value of x is x = 40°.
Hence, the answer is x = 40°.