ACT/SAT Math Problem: Solve it with John Oh

A-List’s Director Curriculum Development, John Oh, walks us through an ACT Math question that has multiple explanations!

The degree measurements of the interior angles of a triangle form an arithmetic sequence with the common difference 10°. What is the first term of the sequence?
 
A.            80°
B.            60°
C.            50°
D.            40°
E.            30°

Many of my students just skip this question because “I don’t remember the formula for an arithmetic sequence.” But to use a_n=a_1+d(n-1) is probably the worst way to solve this question. Instead, one could just render an algebraic expression and solve for x.

x + (x + 10) + (x + 20) = 180
3x + 30 = 180
x = 50 (C.)

Or, one could just Backsolve. Let’s start with middle choice C: 50. So, if the first angle is 50° and the common difference is 10°, then the second angle differs from the first angle by 10; ergo, it’s 60°. Of course, the third angle differs from the second angle by 10 as well; ergo, it’s 70°. Now what? Well, the question tells us that these are ‘the degree measurements of the interior angles of a triangle.” Are they? Yes: 50 + 60 + 70 = 180.