Angles and Polygons - Short Problems

A collection of short Stage 3 problems on Angles and Polygons



Weekly Problem 47 - 2011

Challenge Level: Challenge Level:1

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

Weekly Problem 8 - 2008

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

Weekly Problem 13 - 2008

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

Weekly Problem 18 - 2008

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

Weekly Problem 38 - 2008

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

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

Weekly Problem 39 - 2008

Stage: 3 Challenge Level: Challenge Level:1

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

Weekly Problem 45 - 2008

Stage: 3 Challenge Level: Challenge Level:1

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 50 - 2008

Stage: 3 Short Challenge Level: Challenge Level:1

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

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

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

Stage: 3 Challenge Level: Challenge Level:1

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

Weekly Problem 21 - 2009

Stage: 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 33 - 2009

Stage: 3 Short Challenge Level: Challenge Level:1

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

Stage: 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 21 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 39 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 44 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 18 - 2011

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 1 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 1 - 2014

Weekly Problem 11 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 11 - 2014

Weekly Problem 19 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 19 - 2014

Weekly Problem 51 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 51 - 2014

Weekly Problem 40 - 2015

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Weekly Problem 40 - 2015

Weekly Problem 46 - 2015

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Weekly Problem 46 - 2015