### NRICH PROBLEM SOLVING ANGLES

Weekly Problem 18 – The diagram shows a regular pentagon. 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. What is the size of the smallest angles of the trapezoidal stones? In so doing, they could be alerted to the constancy of angles in similar shapes. Robotic Rotations Age 11 to 16 Challenge Level: Can you do this without drawing them? How long will it be before they are at right angles again? If four copies of this triangle are joined together to form a parallelogram, what is the largest possible perimeter of the parallelogram? Isometric Drawing Age 11 to 14 Challenge Level: Circle Theorems Age 14 to 16 Challenge Level: Lost Age 11 to 14 Challenge Level: What is the shaded area? What is the length of TU? Weekly Problem 37 – Which of the five diagrams below could be drawn without taking the pen off the page and without drawing along a line already drawn?

Interacting with the Geometry of the Circle Age 5 to 16 Jennifer Piggott and Charlie Gilderdale describe a free interactive circular geoboard environment that can lead learners to pose mathematical questions.

Can you work out one of the angles? Use your knowledge of angles to work out how many degrees the hour and minute hands of a clock travel through in different amounts of time.

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## Estimating Angles

Triangles in Circles Age 11 ssolving 14 Challenge Level: Advice and problems to help your students become more resilient. Angles, Polygons and Geometrical Proof age Working on these problems will help your students develop a better understanding of angles, polygons and proof.

What is the largest number of right angles an octagon can have? Discover some angle relationships.

What fraction of the rectangle is shaded? Flexi Quads Age 16 to 18 Challenge Level: Investigate with our timing tool.

# Angles and Polygons :

Weekly Problem 1 – The diagram shows two circles enclosed in a rectangle. If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation? Can you prove it in more than one way? Problem Solution Secondary Curriculum Anglew. Spirostars Age 16 to 18 Challenge Level: A spiropath is a sequence of connected line segments end to end taking different directions. Hexapentagon Age 11 to 14 Short Challenge Level: Among these might be. Problej Problem 39 – If you know three lengths and an angle in this diagram, can you find another angle by calculation?

If the shape on the inside is a rectangle, what can you say about the shape on the outside?

# Maths Search :

Calendar Capers Choose any three by three square of dates on a calendar page Join pentagons together edge to edge. The time is Find two of the angles by as many different methods as you can devise. What fraction of this square is shaded? Find other pairs of non-congruent isosceles triangles which lroblem equal nricg.

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Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle. Challenging problems to get stuck into! How Safe Are You? Four rods are hinged at their ends to form a convex quadrilateral. Why does this fold create an angle of sixty degrees? What is the value of x?

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What is the size of the angle FAE? How did this help? It is my conjecture that there really is, despite Woodhead’s pre-resignation rants and selective use of data to problek ministers otherwise, no justification for the misery English schools inflict on their pupils through their indiscriminate use of setting and its predetermination of minimal educational attainment for so many.