Let's investigate

Without measuring, work out the angle at X.

1) An ancient civilization hidden within a distant mountain range, carved their writing into clay tablets as a series of angles. Each size of angle, matches a letter in our alphabet or a digit from 0 to 9.
This clay tablet has been smashed. Work out the letter or number on each piece and then rearrange them to discover the word.

(1) The word is ...........................

2) Draw the angles that would write the word "triangle.

3) Four children are making triangles using sticks.

Can everyone make the triangle they want? Explain your answer.

4) Each of these pies has been cut into unequal slices. Work out the missing angle on each pie, without measuring.

5) Imagine a pie was cut into equal slices. What would be the angle of each piece if it were cut into:
(a) 2 pieces
(b) 3 pieces
(c) 4 pieces
(d) 5 pieces
(e) 6 pieces
(f) 7 pieces
(g) 8 pieces
(h) 9 pieces
(i) 10 pieces
(j) 11 pieces
(k) 12 pieces

6) Sebastian drew a triangle. He split the triangle into two right-angled triangles by drawing a dotted line.
Without measuring the angles, work out the angles (a), (b) and (c).

7) Find the angles marked with a shape symbol.