# Angles - August 2005, All Stages

## Problems

### Right Angle Challenge

##### Stage: 1 Challenge Level:

How many right angles can you make using two sticks?

### Sweeping Hands

##### Stage: 2 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.

### Chippy's Journeys

##### Stage: 2 Challenge Level:

Chippy the Robot goes on journeys. How far and in what direction must he travel to get back to his base?

### Nine-pin Triangles

##### Stage: 2 Challenge Level:

How many different triangles can you make on a circular pegboard that has nine pegs?

### Triangles All Around

##### Stage: 2 Challenge Level:

Can you find all the different triangles on these peg boards, and find their angles?

### Triangle Pin-down

##### Stage: 2 Challenge Level:

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

##### Stage: 3 Challenge Level:

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

### Triangles in Circles

##### Stage: 3 Challenge Level:

How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?

### Right Angles

##### Stage: 3 Challenge Level:

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

### Subtended Angles

##### Stage: 3 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?

##### Stage: 4 Challenge Level:

Make five different quadrilaterals on a nine-point pegboard, without using the centre peg. Work out the angles in each quadrilateral you make. Now, what other relationships you can see?

### Sine and Cosine for Connected Angles

##### Stage: 4 Challenge Level:

The length AM can be calculated using trigonometry in two different ways. Create this pair of equivalent calculations for different peg boards, notice a general result, and account for it.

### Figure of Eight

##### Stage: 4 Challenge Level:

On a nine-point pegboard a band is stretched over 4 pegs in a "figure of 8" arrangement. How many different "figure of 8" arrangements can be made ?

### Octa-flower

##### Stage: 5 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?

### Cubestick

##### Stage: 5 Challenge Level:

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.

### Walls

##### Stage: 5 Challenge Level:

Plane 1 contains points A, B and C and plane 2 contains points A and B. Find all the points on plane 2 such that the two planes are perpendicular.