Two regular pentagons, one of which has an extended side. What’s the angle α?

# Category: Beginner

## The happy couple

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

## The beach ball

What fraction of the regular dodecagon is red?

## Drilling site

A blue flagpole is erected near a drilling site. Lines are drilled perpendicular to the flagpole guy wires and meet at the bottom of the orange drilling pipe. What is the ratio of distances green to red?

## A devious cevian

A triangle with a cevian. It is split into two similar triangles. What is angle ABC?

## Triangulation

A regular dodecagon contains a yellow square. Find the three angles α, β and γ.

## Paranoid centroid

A square is divided in four triangles of which the red centroids are shown. What fraction is green?

## The Siamese triplet

Three circles with a common intersection point and two triangles. What is α : β?

## Nearly the same

Two rectangles are positioned with the side of each one along the diagonal on the other. Furthermore, two of their sides have the same length, as marked. What is the quotient of areas (A+B)/(C+D)?

## The blue lagoon

Five congruent brown triangles inside a rectangle. What fraction is brown?