What is X and Y? I will give brainliest to whoever shows work and explains how to do the problem and if its correct.

x = 5()

y = 10

Step-by-step explanation:

1st, we need to find the angles on the triangle before we can solve for side lengths.

Line Y is intercepted by line X which forms 2 supplementary angles.

These angles add up to 180 so 180 - 150 = 30 therefor the angle is 30 degrees

Next, using the vertical angle theorem, we see that there is a right angle and using this theorem, we can determine this is a right triangle and that angle is 90 degrees

Using the triangle sum theorem, we know a triangle's sum is = to 180 degrees

90 + 30 + x = 180

120 + x = 180

x = (180 - 120)

x = 60

We now determined this is a 90-60-30 triangle

The opposite of the 30 degree angle is the 5 unit measurement

According to this theorem 5 is equal to x because the side opposite of the 30 degree angle is = to x (not the side variable, the variable for this theorem)

We now solve the rest

x = 5

2x (opposite of 90 degrees) = 10

5x = 5() (This is in its simplest form)

So now based upon this,

x = 5()

y = 10

step-by-step explanation: