Angles - points, lines and parallel lines

problem
Right angles

Age

11 to 14

Challenge level

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
problem
Subtended angles

Age

11 to 14

Challenge level

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?
problem
Triangles in circles

Age

11 to 14

Challenge level

Can you find triangles on a 9-point circle? Can you work out their angles?
problem
Angular reflection

Age

11 to 14

Challenge level

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?
problem
Sweeping hands

Age

7 to 11

Challenge level

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.
problem
Right angle challenge

Age

5 to 7

Challenge level

How many right angles can you make using two sticks?
problem
Octa-flower

Age

16 to 18

Challenge level

Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?
problem
Isosceles meld

Age

11 to 14

Challenge level

Weekly Problem 9 - 2012
What is the angle QPT in this diagram?
problem
Flower

Age

16 to 18

Challenge level

Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.
problem
Lunar angles

Age

16 to 18

Challenge level

What is the sum of the angles of a triangle whose sides are circular arcs on a flat surface? What if the triangle is on the surface of a sphere?