Mathematics > Standard Multiple Choice
Read the following SAT test question and then click on a button to select your answer.
In the figure above, x = 60 and y = 40. If the dashed lines bisect the angles with measures of x° and y°, what is the value of z?
(A) 25
(B) 35
(C) 40
(D) 45
(E) 50
The correct answer is E
Explanation
First, add the labeled points A, B, C, D, E, and O to the figure, as shown above. Then segment 
bisects 
, so 
, and
. Thus, = 30°. Similarly, 
, because 
and 
are of equal measure and the sum of their measures is y° = 40°. From the figure, it follows that 
. Therefore, z = 50.