2015 AMC 10B Problems/Problem 22
Contents
Problem
In the figure shown below, is a regular pentagon and
. What is
?
Solution 1
Triangle is isosceles, so
.
since
is also isosceles. Using the symmetry of pentagon
, notice that
. Therefore,
.
Since ,
.
However, since
must be greater than 0.
Notice that .
Therefore,
Solution 2
Note that since is a regular pentagon, all of its interior angles are
. We can say that pentagon
is also regular by symmetry. So, all of the interior angles of
are
. Now, we can angle chase and use trigonometry to get that
,
, and
. Adding these together, we get that
. Because calculators were not permitted in the 2015 AMC 10B, we can not use a calculator to find out which of the options is equal to
, but we can find that this is closest to
.
See Also
2015 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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