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HKD1710

In the figure above, what is the value of 2x - y?

(A) 0
(B) 15
(C) 30
(D) 45
(E) 60


Attachment:
Angles.JPG
Here's a different approach:

Since angles in a triangle must add to 180°, the 3rd angle in the blue triangle must be 105°


Since angles on a line must add to 180°, we know the two angles below are each75°


Finally, since angles in a triangle must add to 180° . . .

. . . we can see that x = 15° and y = 15°

What is the value of 2x - y?
2x - y = 2(15°) - 15° = 30° - 15° = 15°

Answer: B

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Looking at the two triangles, both are right angles (a 90 degree interior angle). We managed to see that:

In one of the triangles, which includes X, we have:

30 + X = 45, so X = 15.

In the other triangle, which includes Y, we have:

45 + Y = 60, so Y = 15

Then 2X - Y = 15°

Answer B
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