Categories
Beginner

The pentagon push

Two regular pentagons share a vertex. What’s the angle α?

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Intermediate

The bishop’s hat

Two overlapping regular pentagons share two vertices. What fraction is the overlap area?

Categories
Advanced

Tympanum II

A regular pentagon with a diagonal. What is the top angle of the isosceles triangle?

Categories
Advanced

The tympanum

A regular pentagon with a diagonal and an extended side. What is the top angle of the isosceles triangle?

Categories
Intermediate

Daft Mouse

A square with two attached regular pentagons. A side and a diagonal are extended. What’s the angle?

Categories
Beginner

The spinning top

An equilateral triangle stacked on a pentagon. What’s the angle?

Categories
Intermediate

The Pentagon peaches

Five equally sized peaches are closely packed in a pentagon-shaped box. Their midpoints are the vertices of a smaller pentagon. What fraction is shaded?