Is it equilateral?

In the diagram below, \(ABDC\) is a square. Angles \(ACE\) and \(BDE\) are both 75°.
Is triangle \(ABE\) equilateral? Why/why not?

Show answer

17 December

The number of degrees in one internal angle of a regular polygon with 360 sides.

Ticking clock

Is there a time of day when the hands of an analogue clock (one with a second hand that moves every second instead of moving continuously) will all be 120° apart?

Show answer & extension

Tags: angles, time


In the diagram, B, A, C, D, E, F, G, H, I, J, K and L are the vertices of a regular dodecagon and B, A, M, N, O and P are the vertices of a regular hexagon.
Show that A, M and E lie on a straight line.

Show answer & extension

Three squares

Source: Numberphile
The diagram shows three squares with diagonals drawn on and three angles labelled.
What is the value of \(\alpha+\beta+\gamma\)?

Show answer & extension


Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles


cryptic crossnumbers triangle numbers differentiation median wordplay digits parabolas area star numbers pascal's triangle squares books scales digital clocks addition mean coordinates percentages integers probability 2d shapes perfect numbers speed probabilty shapes symmetry sport triangles balancing crossnumbers range dice means division lines rugby volume proportion clocks menace ellipses irreducible numbers geometry rectangles christmas complex numbers regular shapes advent surds angles routes chess unit fractions taxicab geometry hexagons remainders elections square numbers crosswords quadratics trigonometry sequences people maths tiling dodecagons cryptic clues cube numbers crossnumber number bases partitions spheres doubling palindromes dominos the only crossnumber calculus colouring planes games arrows cards sum to infinity perimeter products prime numbers multiples floors averages time sums algebra functions factorials folding tube maps numbers circles coins gerrymandering polygons logic odd numbers dates multiplication indices 3d shapes shape chocolate chalkdust crossnumber square roots ave integration factors graphs fractions grids money


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020