Answer:
x = 5([tex]\sqrt{3}[/tex])
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([tex]\sqrt{3}[/tex]) (This is in its simplest form)
So now based upon this,
x = 5([tex]\sqrt{3}[/tex])
y = 10
