每日一题

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 degrees and y degrees, what is the value of z?

(A) 25
(B) 35
(C) 40
(D) 45
(E) 50

答案和解析

答案：E

解析：

First, add the labeled points A, B, C, D, E, and O to the figure, as shown above. Then segment line O B bisects angle A O C, so measure of angle A O B = measure of angle B O C, and measure of angle A O B + measure of angle B O C = x degrees = 60 degrees. Thus, measure of angle A O B = measure of angle B O C = 30 degrees. Similarly, measure of angle C O D = measure of angle D O E = 20 degrees, because angle C O D and angle D O E are of equal measure and the sum of their measures is y degrees = 40 degrees. From the figure, it follows that z degrees = measure of angle B O C + measure of angle C O D = 30 degrees + 30 degrees = 50 degrees. Therefore, z = 50.