First look at the point of intersection of those three diagonals. Angle a is opposite the 15 degree angle and angle b is opposite
the third angle of a triangle whose other angles have measures of 55 degrees and 40 degrees.
These opposite or vertical angles must be congruent, so a = 15 and
C
In a diagram with angles, look for how the angles relate to each other.
Evaluate each statement.
You are left with only one answer choice. If you’re curious, here’s Statement III:
51.
Must a + b = 180°? No. You know that a, b, and the angle separating them sum to 180°, since they form a straight line, but
you cannot say that a + b = 180°. Eliminate (A) and (E).
I.
II. Must c + e = 180°? No. There is no necessary relationship between these angles. Eliminate (B) and (D).
Must c + d + e = 180°? Yes. Think of vertical angles. The angle across from c must equal c and the same holds true for d
and e. These angles form a triangle in the middle of the figure. Since the angles of a triangle must sum to 180°, c + d + e =
180°. (C) is correct.
III.
F
Any time you see intersecting lines, look for vertical angles and supplementary angles (angles that make a straight line).
Vertical angles are equal, so 150° = (4a + 2)°.
a − b = 37 − 30 = 7, answer choice (F). Be sure you answer the right question—(G) is b and (H) is a, but neither of those is
what you are looking for.
52.
