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Home > College Board Tests > The Official SAT Question of the Day

Sunday, September 6

Here's Why:
$MATH GRAPHIC$

Note: Figure not drawn to scale.

First, add the labeled points A, B, C, D, E, and O to the figure, as shown above. Then segment $line over OB$ bisects $angle$ AOC, so m $angle$ AOB = m $angle$ BOC, and m $angle$ AOB + m $angle$ BOC = x° = 60°. Thus, m $angle$ AOB = m $angle$ BOC = 30°. Similarly, m $angle$ COD = m $angle$ DOE = 20°, because $angle$ COD and $angle$ DOE are of equal measure and the sum of their measures is y° = 40°. From the figure, it follows that z° = m $angle$ BOC + m $angle$ COD = 30° + 20° = 50°. Therefore, z = 50.
Difficulty: Easy
Question Type: Standard Multiple Choice
(Mathematics)