Test 3 Section 3 #18

First, here’s a mockup of the figure (not to scale):

You’re told that 180 – *z* = 2*y*, and then you’re told that *y* = 75. (This is typical of the SAT: give you the information in the reverse order in which you should use it.) So let’s solve for *z*, and then mark up the figure a bit.

180 – *z* = 2(75)

180 – *z* = 150

–*z* = –30

*z* = 30

To move forward from here, you need to remember the base angle theorem: in isosceles triangles, the angles across from the congruent sides are also congruent. So the blue angles and the red angles below are congruent.

We want *x*, so let’s figure out what those red angles are (I’ll use *a* for them):

30 + 2*a* = 180

2*a* = 150

*a* = 75

If the red angles each measure 75°, then remembering that a straight line measures 180°, we can solve for *x*:

75 + *x* = 180

*x* = 105