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


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


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