Attaching some images, self-reference solution that anyone can feel free to use.
The first image is the original question in illustrated form.
Based on this first image, we can come up with the second image which lets us fill in a lot of useful angle details. First, we get \(∠CMB = 180 - 2x\) because angles in a line must add up to 180. Then because angles in a triangle add up to 180, we can calculate that \(∠MCB = 180 - 90 - (180 - 2x) = 180 - 90 - 180 + 2x = 2x - 90\). Then because we know that all corners of a rectangle are 90 degrees, we can calculate that \(∠MCD = 90 - (2x - 90) = 90 - 2x + 90 = 180 - 2x\). Once again using the property of 180 degrees in a triangle, we can finally calculate that \(∠MDC = 180 - x - (180 - 2x) = 180 - x - 180 + 2x = x\).
This gives us useful information about the sides that we can see in the third image. Now that we know that triangle DMC has 2 of the same angles, it must be an isosceles triangle, and the sides opposite the equal angles are also equal in length. Since CD is 6 because it is a side of the rectangle, MC is also 6. Then, we can calculate that \(MB = \sqrt{6^2 - 3^3} = 3\sqrt{3}\) using the Pythagorean Theorem.
This triangle represents the properties of a 30-60-90 triangle, where the hypotenuse is \(2s\) (aka \(s = 3\)), the longer non-hypotenuse side across from the 60 degree angle is \(s\sqrt{3}\) (aka \(3\sqrt{3}\))and the shorter side opposite the 30 degree angle is s (aka \(3\)). Therefore, we know that ∠MCB is 60 degrees and ∠CMB is 30 degrees.
Finally, we can calculate for x. (you can use either ∠MCB or ∠CMB and it will produce the same result).
If using ∠CMB:
\(180 - 2x = 30\)
-> \(2x = 150\)
-> \(x = 75\)
If using ∠MCB:
\(2x - 90 = 60\)
-> \(2x = 150\)
-> \(x = 75\)
Answer choice E is correct. Hope this helps like it helped me!