(SAT Prep) Find the value of x.

x = 155

Step-by-step explanation:

First find the missing angle in the smaller triangle.

We know that the sum of the angles in a triangle is 180 so 35 + 90 + the missing angle = 180 so 180 - (35+90) = 180 - 125 = 55

Since the line above is a straight line, the sum of the angles must equal 180 so 55 + 60 + ? = 180. So 180 - 115 = 65.

The triangle is a right triangle so that means on of the angles is 90. So 65 + 90 = 155, so we have 180 - 155 = 25.

The angle that x is on is also a straight line so that means the angles must add up to 180 so 180 - 25 = 155.

Recall that triangles add to 180 degrees.
In the left triangle, the angles are 35 + 90 + angle = 180. The third angle of the left triangle is 55 degrees.

Now recall that angles drawn from a straight line all add up to 180 degrees
So 55 + 60 + third angle = 180. Thus, the third angle is 65 degrees.

Within the middle triangle, we now have 2/3 of the angles. 90 + 65 + third angle = 180. Thus, the third angle is 25 degrees.

25 degrees is right next to angle X. As we have already stated, they add up to 180 when adjacent.

So 180-25 = 155 degrees, the value of angle X.

1425 is the min 1575 is the max