What fraction of a revolution have you turned through if you stand facing

(i) north and turn clockwise to face west?

(ii) south and turn anti-clockwise to face east?

(iii) east and turn clockwise (or anti-clockwise) to face west?

Also find the number of right angles turned in each case.

One complete revolution = 4 right angles = 360°.

So, $\dfrac{1}{4}$ revolution = 1 right angle = 90°.

(i) Facing north and turning clockwise to face west:

The sequence is: North → East → South → West.

This is 3 right angles or $\dfrac{3}{4}$ of a revolution.

∴ Fraction of revolution = $\dfrac{3}{4}$ and number of right angles = 3.

(ii) Facing south and turning anti-clockwise to face east:

The sequence is: South → East.

This is 1 right angle or $\dfrac{1}{4}$ of a revolution.

∴ Fraction of revolution = $\dfrac{1}{4}$ and number of right angles = 1.

(iii) Facing east and turning (clockwise or anti-clockwise) to face west:

This is 2 right angles or $\dfrac{1}{2}$ of a revolution.

∴ Fraction of revolution = $\dfrac{1}{2}$ and number of right angles = 2.