Question of the Day

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10/11 , 11/8

Sep
1
2014
3,174 responses
Question of the Day Statistics
Number Answered
Correct 2,506
Incorrect 668
78% correct

Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

11-3-2013-M41016_1.png

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?

Answer Choices

Hint

You can use the fact that the dashed lines are angle bisectors to write z in terms of x and y.

Question of the Day

Can you answer today's question?

Register Next Tests:
10/11 , 11/8

Sep
1
2014
3,174 responses
Question of the Day Statistics
Number Answered
Correct 2,506
Incorrect 668
78% correct

Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

11-3-2013-M41016_1.png

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?

Answer Choices

Answer

Image

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.