As you can see, he uses one square for Stage 1, three squares for Stage 2 and six for Stage 3. How many squares should he use for the sixth stage?

21

Step-by-step explanation:

stage 1:  1

stage 2: 3

stage 3: 6

the pattern is that the number of squares increases everytime by the stage number it is. for example stage 2 has 3 squares. to find stage 3 you start off with 3 squares (from stage 2), and add the stage number (stage 3). 3+3=6 so stage 3 has 6 squares.

stage 4: 10 (6+4)

stage 5: 15 (10+5)

stage 6: 21 (15+6)

by definition, an arc subtended by a central angle of some given measure has the same measure. so .