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 

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2019