SAT Math Multiple Choice Practice Question 193: Answer and Explanation

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Question: 193

17.

What is the sum of the angles marked a, b, c, d, and e in the preceding diagram?

A. 180°
B. 270°
C. 360°
D. 540°
E. 720°

Correct Answer: C

Explanation:

C. To solve this problem, you have to remember that the sum of the exterior angles of any shape is always 360 degrees. (See Chapter 16 to review this idea.) If you don't remember that handy tip, you can also calculate the sum of the exterior angles for this pentagon. First, you determine what the sum of the interior angles is. Pick one vertex and draw straight lines to each of the other vertices, creating three triangles. You know that each triangle contains 180 degrees, so the pentagon, with three triangles, has 3 × 180° = 540°. You also know that each straight line has 180°, so each exterior angle plus its interior angle has 180°. There are five exterior angles, so the sum of all the interior and exterior angles is 5 × 180° = 900°. Now all you need to do is subtract: The sum of all the interior and exterior angles minus the sum of the interior angles gives you the sum of the exterior angles: 900° - 540° = 360°.

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