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The figure shows that l is parallel to m. What is ∠ x+∠

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by Max@Math Revolution » Wed Oct 16, 2019 1:16 am
[GMAT math practice question]

The figure shows that l is parallel to m. What is ∠ x+∠ y+∠ z+∠ p+∠ q+∠ r?

A. 90
B. 100
C. 160
D. 180
E. 190


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by GMATGuruNY » Thu Oct 17, 2019 2:45 am
For any polygon with n sides, the sum of the interior angles = (n-2)(180).
In a DECAGON -- a polygon with 10 sides -- the sum of the interior angles = (10-2)(180) = 1440.
If a regular decagon -- a decagon with 10 equal sides and 10 equal angles -- the degree measurement of each angle = 1440/10 = 144.

To solve the problem above, we can redraw the figure so that x, y, z, p, q and r are exterior angles for a regular decagon, as shown in the figure below:
Image
In the redrawn figure, x+y+z+p+q+r = 18+36+36+36+36+18 = 180.

The correct answer is D.
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by Max@Math Revolution » Fri Oct 18, 2019 1:40 am
=>

When we draw parallel lines passing through the point Q, we have the following figure.
Then we have < x+< y+< z+< p+< q+< r = 180°.

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Therefore, D is the answer.
Answer: D
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