Lines and Angles

Geometry: Lines and Angles

Read the following SAT test question and then select the correct answer.

For every math problem, you should use the Knowsys method: read the question carefully, identify the bottom line, assess your options, attack the problem, and loop back to verify that the answer you found addresses the bottom line. 

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?

Geometry questions often include figures with multiple variables.  When you are assessing your options, realize that you can estimate values with figures that are drawn to scale, but that figures that are not drawn to scale may be misleading and estimation may result in a wrong answer.  When you are prepared to attack your problem, it is especially important to write your scratch work so that you can see how each number you find relates to the figure.  The easiest way to do that is to add the values you find to the figure.

The bottom line that you are solving for is z, but the information you are given is about x and y. First look at x.  Your ability to solve this problem hinges on your knowledge that “bisect” means “divides in half.” You know that x totals 60, so half of 60 is on each side of the dashed line that bisects x. 

60 ÷ 2 = 30

Likewise, you know that y totals 40, so half of 40 is on each side of the dashed line that bisects y.

40 ÷ 2 = 20

Now look at z. This variable overlaps half of x and half of y.  You just solved for each of these, so add them together.

30 + 20 = 50

Loop back to make sure that you solved the question that was asked and then match your answer choice to the answers that are given.

(A) 25

(B) 35

(C) 40

(D) 45

(E) 50

The correct answer is (E).


On sat.collegeboard.org, 81% of responses were correct.


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