Test 3 Section 3 #18

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

You’re told that 180 – z = 2y, 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 + 2a = 180
2a = 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