## Triangles

In the figure above, what is the sum, in terms of *a*, of angles *b,* *c*, *d*, and *e*?

A. * a*

B. 2*a*

C. 180 – *a*

D. 180 – 2*a*

E. 360 – *a*

## Knowsys Method

**Read the problem carefully.** Notice that the image is drawn to scale because it does not indicate otherwise.

**Identify the bottom line.** *b* + *c *+ *d* + *e* = ?

**Assess your options. ** If you find yourself stumped on a triangle problem on the SAT, run through the facts and rules you know about triangles and determine whether any of this knowledge applies to the problem at hand. This problem is categorized as a “hard” level problem, but knowing one simple fact about triangles makes this problem easy to solve.

FACT: The exterior angle d equals the sum of the opposite interior angles *a* and *b*.

So, *d* = *a* + *b*.

**Attack the problem.**

Angle *a* is an exterior angle to both triangles in the image. That means:

*a* = *b* + *c*

AND

*a* =* d* + *e*

Therefore:

*b* + *c* +* d* + *e *= 2*a*

**Loop back. ** You found the solution to the bottom line.

The correct answer is B.

This is a hard level problem.

**Want some help reviewing the math concepts you need to master? **Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.