Pentagonal Pyramid

The pyramid VABCDE has a regular pentagon ABCDE as its base, and all five lateral faces are equilateral triangles. What is the measure of angle AVC.

Source: NCTM Mathematics Teacher

SOLUTION

Triangle AVC\cong triangle ABC by SSS
AC=AC reflexive property
AB=AV all five lateral faces are equilateral triangles
CB=CV same reason

\angle AVC=\angle ABC
=\frac{540^\circ}{5}
=108^\circ

Answer: 108^\circ

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About mvtrinh

Retired high school math teacher.
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