A square and a regular pentagon share a vertex. What’s the angle α?

# Tag: angle

## Orthogonal partial eclipse

Two circles are orthogonal (tangents at intersections are perpendicular). How must the points A and B be related?

## Folding to pyramid

A square and an equilateral triangle. The square is folded as shown. What is the angle α?

## Outside the pentagon II

A regular pentagon and two equilateral triangles. What’s the angle α?

Two squares and some line segments. Find the relation between the angles α and β.

## What’s your angle?

Six squares are placed as shown. What’s the angle α?

## Steam roller

Two intersecting circles. Express the lengths b and the common tangent d in terms of c (the distance between the centres) and the angles β and γ.

## Fair scoop

What is the ratio of areas purple : orange if the cone angle is 45°, and the circular arc is a semicircle?

## Six six four

Two regular hexagons and a square. What’s the angle α?

## Square offspring

Three squares and two line segments. What’s the angle α?