## 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: $108^\circ$