Weekly Problem 26 - 2006

How many right angled triangles are formed by the points in this diagram?

Weekly Problem 18 - 2011

Draw an equilateral triangle onto one side of a square. Can you work out one particular angle?

Weekly Problem 45 - 2008

The diagram shows a regular pentagon with two of its diagonals. If all the diagonals are drawn in, into how many areas will the pentagon be divided?

Weekly Problem 28 - 2013

Two lines meet at a point. Another line through this point is reflected in both of these lines. What is the angle between the image lines?

Weekly Problem 9 - 2012

What is the angle QPT in this diagram?

Weekly Problem 33 - 2009

In a village the pub, church and school are at different lengths and bearings from each other. What is the bearing of the school from the church?

Weekly Problem 35 - 2009

Two equilateral triangles have been drawn on two adjacent sides of a square. What is the angle between the triangles?

Weekly Problem 16 - 2007

Can you figure out how far the robot has travelled by the time it is first facing due East?

Weekly Problem 30 - 2013

What is the angle $x$ in the star shape shown?

Weekly Problem 21 - 2010

How many diagonals can you draw on this square...

Weekly Problem 18 - 2007

A regular pentagon together with three sides of a regular hexagon form a cradle. What is the size of one of the angles?

Weekly Problem 40 - 2013

Given three sides of a quadrilateral, what is the longest that the fourth side can be?

Weekly Problem 39 - 2010

If you know three lengths and an angle in this diagram, can you find another angle by calculation?

Weekly Problem 21 - 2009

What is the angle between the two hands of a clock at 2.30?

Weekly Problem 37 - 2013

Which of the statements about diagonals of polygons is false?

Weekly Problem 44 - 2010

Extend two of the sides of a nonagon to form an angle. How large is this acute angle?

Weekly Problem 1 - 2006

The diagram shows two circles enclosed in a rectangle. What is the distance between the centres of the circles?

Weekly Problem 39 - 2008

How big is the angle between the hour hand and the minute hand of a clock at twenty to five?

Weekly Problem 7 - 2013

Three of the angles in this diagram all have size $x$. What is the value of $x$?

Weekly Problem 33 - 2006

A square is inscribed in an isoscles right angled triangle of area $x$. What is the area of the square?

Weekly Problem 2 - 2009

The 16 by 9 rectangle is cut as shown. Rearrange the pieces to form a square. What is the perimeter of the square?

Weekly Problem 53 - 2012

ABCDEFGHI is a regular nine-sided polygon (called a 'nonagon' or 'enneagon'). What is the size of the angle FAE ?

Weekly Problem 38 - 2008

A quadrilateral can have four right angles. What is the largest number of right angles an octagon can have?

Weekly Problem 51 - 2012

Each interior angle of a particular polygon is an obtuse angle which is a whole number of degrees. What is the greatest number of sides the polygon could have?

Weekly Problem 47 - 2011

Place equal, regular pentagons together to form a ring. How many pentagons will be needed?

Weekly Problem 15 - 2012

How many of the five properties can a heptagon have?

Weekly Problem 52 - 2012

An irregular hexagon can be made by cutting the corners off an equilateral triangle. How can an identical hexagon be made by cutting the corners off a different equilateral triangle?

Weekly Problem 27 - 2013

The diagram shows a parallelogram inside a triangle. What is the value of $x$?

Weekly Problem 50 - 2008

The lengths SP, SQ and SR are equal and the angle SRQ is x degrees. What is the size of angle PQR?

Weekly Problem 53 - 2007

The diagram shows a regular pentagon and regular hexagon which overlap. What is the value of x?

Weekly Problem 1 - 2014

The diagram shows a regular hexagon inside a rectangle. What is the sum of the four marked angles?

Weekly Problem 8 - 2008

In how many ways can a square be cut in half using a single straight line cut?

Weekly Problem 11 - 2014

The diagram shows a parallelogram and an isosceles triangle. What is the size of angle TQR?

Weekly Problem 13 - 2008

The diagram shows three squares drawn on the sides of a triangle. What is the sum of the three marked angles?

Weekly Problem 19 - 2014

The diagram shows a rhombus and an isosceles triangle. Can you work out the size of the angle JFI?

Weekly Problem 26 - 2007

The diagram shows two equilateral triangles. What is the value of x?

Weekly Problem 45 - 2007

What is the obtuse angle between the hands of a clock at 6 minutes past 8 o'clock?

Weekly Problem 18 - 2008

The diagram shows a regular pentagon. Can you work out the size of the marked angle?

Weekly Problem 46 - 2015

The diagram shows two parallel lines and two angles. What is the value of x?

Weekly Problem 8 - 2016

Can you work out the size of the angles in a quadrilateral?

Weekly Problem 29 - 2013

An equilateral triangle is drawn inside a rhombus, both with equal side lengths. What is one of the angles of the rhombus?

Weekly Problem 40 - 2015

In the diagram, $PT = QT = TS$ and $QS = SR$. What is the value of $x$?

Weekly Problem 27 - 2007

Ten stones form an arch. What is the size of the smallest angles of the trapezoidal stones?

Weekly Problem 17 - 2016

The diagram shows an equilateral triangle touching two straight lines. What is the sum of the four marked angles?

Weekly Problem 10 - 2012

If you know how long Meg's shadow is, can you work out how long the shadow is when she stands on her brother's shoulders?

Weekly Problem 33 - 2016

In the diagram, six circles of equal size touch adjacent circles and the sides of the large rectangle. What is the perimeter of the large rectangle?

Weekly Problem 50 - 2012

The diagram shows a regular dodecagon. What is the size of the marked angle?

Weekly Problem 41 - 2014

Three straight lines divide an equilateral triangle into seven regions. What is the side length of the original triangle?