In the figure above, ABCDE is a regular pentagon with side of length 2.

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In the figure above, ABCDE is a regular pentagon with side of length 2. What is the xcoordinate of D ?
4
.
9
0
(a) 2.62
(b) 3.62
(c) 3.73
(d) 3.90
(e) 4.90
Correct Answer: B
Explanation:
The sum of the measures of the interior angles of a regular pentagon is equal to
3 x 180 = 540°. Each interior angle has a measure of 108°. Using supplementary
angles,
has a measure of 72°. You can use right triangle trigonometry to find
the x-coordinate of point D.
Since
EF = 2 cos 72°
0.62. Since the length of each side of the
pentagon is 2, the x-coordinate of point E is 3. Putting the information together
tells us that the x-coordinate of point D is 3.62. The correct answer is (B).

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