Weekly Problem 47 - 2011

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

Weekly Problem 9 - 2012

What is the angle QPT in this diagram?

Weekly Problem 15 - 2012

How many of the five properties can a heptagon have?

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 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 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 27 - 2013

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

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 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 30 - 2013

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

Weekly Problem 40 - 2013

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

Weekly Problem 37 - 2013

Which of the statements about diagonals of polygons is false?

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

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

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

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

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

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?

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

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 6 - 2009

In a triangle the smallest angle is 20 degrees. What is the largest possible angle in the triangle?

Weekly Problem 21 - 2009

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

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?

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

Weekly Problem 21 - 2010

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

Weekly Problem 39 - 2010

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

Weekly Problem 44 - 2010

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

Weekly Problem 18 - 2011

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

Weekly Problem 7 - 2013

Three of the angles in this diagram all have size $x$. 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 11 - 2014

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

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 51 - 2014

A square, regular pentagon and equilateral triangle share a vertex. What is the size of the other angle there?

Weekly Problem 40 - 2015

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

Weekly Problem 46 - 2015

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

Weekly Problem 8 - 2016

The diagram shows a quadrilateral $ABCD$, in which $AD=BC$, $\angle CAD=50^\circ$, $\angle ACD=65^\circ$ and $\angle ACB=70^\circ$. What is the size of $\angle ABC$?

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 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 47 - 2016

What is the sum of the six marked angles?

Weekly Problem 28 - 2017

The diagram on the right shows an equilateral triangle, a square and a regular pentagon. What is the sum of the interior angles of the resulting polygon?

Weekly Problem 19 - 2017

In the figure, what is the value of x?

Weekly Problem 37 - 2017

A quadrilateral is divided into two isosceles triangles. Can you work out the perimeter of the quadrilateral?

Weekly Problem 38 - 2017

In the diagram, what is the value of $x$?

Weekly Problem 49 - 2017

Each interior angle in a quadrilateral (apart from the smallest) is twice the previous one. What is the size of the smallest interior angle?