Question

How would I solve for X?

Answer 1

This might get a little complicated...

In a quadrilateral, opposite angles are equal to 180 degrees. This means that the green angles are equal to 180 and the red angles are equal to 180 (See the picture below).
By knowing this, we find that angle Q = 114.

Now we need to find some arc lengths. Since angle Q is an inscribed angle, we can say that arc NML = angleQ * 2. So the measure of arc NML is 228.

This is the total arc length, including the arc that has a length of 118. We need to find the length of arc ML, so we can subtract 118 from our total arc length of 228. This gets us that arc ML = 110.

We now notice that the angle NMQ (which has x) is an inscribed angle, and its corresponding arc is MLQ (which measures 160). Since angle NMQ is half of arc MLQ, we can do the following equation:

NMQ = 1/2(MLQ)
27x-1 = 1/2(160)
Simplified is:
27x-1=80
Add one to each side to get:
27x=81
Divide by 7 to get the long awaited answer of 3
x=3

:)