Find the missing distance in this diagram with two isosceles triangles. Given four of the angles in two triangles, can you find the smallest angle overall? What fraction of the square is shaded? This is a fallacy and, along with teachers carrying piles of books home for marking, performance indicators and level descriptors, is indicative not of pedagogically sound practice but an English tradition which, in general, fails to find a parallel on the continent. What is the size of angle TQR? Weekly Problem 15 – How many of the five properties can a heptagon have? Semi-regular Tessellations Age 11 to 16 Challenge Level:

What if the point goes outside the rectangle? Register for our mailing list. How many right angles can you make using two sticks? Students can discover angle relationships. Find the sum of all of the angles denoted by letters in this diagram.

nrich problem solving angles

Degree Ceremony Age 16 to 18 Challenge Level: How long will it be before they are at right angles again? Isosceles Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8.

In its recent review of the attainment of children at Key Stage 3, the Qualifications and Curriculum Authority QCA, recommended that “teachers should provide pupils with more opportunities to develop familiarity with units of measurement” and “more practice solging reading and using scales”.


Angles Inside

Weekly Problem 38 – A quadrilateral can have four right angles. Can you find the value of x in this diagram? What is the size of angle TQR? Fangs Age 11 to 14 Short Challenge Level: Weekly Problem 8 – Are you able to find triangles such that these five statements are true?

Such invocations concern me, not because I have a principled objection to the sentiments, but because they are presented in ways that suggest that familiarity with units of measurement and practice in using scales are worthwhile ends in themselves. Is there a theorem?

Angles and Polygons :

Can you work out one particular angle? All 5 to 11 7 to 14 11 to 16 14 to 18 Challenge level: The first method is as follows: Register for our mailing list. What mathematics do I need to know to be able to do it?

Find the sum of all of the angles denoted by letters in this diagram.

Can you find triangles on a 9-point circle? What do you notice? Have a good look at these images. Can you make images which show the turnings described?

nrich problem solving angles

To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into prob,em classroom practice. Weekly Problem 13 – The diagram shows contains some equal lengths. Same Length Age 11 to 16 Challenge Level: Angles Inside Age 11 to 14 Challenge Level: Find the distance marked on the diagram.


These questions will make you look at car wheels in a different way! Investigate how this is possible. Stick some cubes together to make a cuboid.

Estimating Angles

An introduction to variables in a familiar setting. The graph below is an oblique coordinate system based on 60 degree angles. What is the sum of the interior angles of the resulting polygon?

nrich problem solving angles

How did this help? Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

Jennifer Piggott and Charlie Gilderdale describe a free interactive circular geoboard environment that can lead learners to pose mathematical questions. Weekly Problem 47 – Xngles is the sum of the six marked angles?

It was drawn on isometric paper.