Chapter 3 Solutions — Angles as Turns

An acute turn is less than 1/4 turn.

Adding two acute turns: each is less than 1/4, so together they are less than 1/2 turn.

But together they could be more than 1/4 turn (obtuse) or exactly 1/4 turn (right angle) depending on the size.

Example: 1/8 turn + 1/8 turn = 2/8 = 1/4 turn = right angle (not acute).

Example: 1/8 turn + 1/6 turn = 7/24 turn (= 105 degrees) = obtuse angle (not acute).

But if both are very small: 1/16 + 1/16 = 1/8 turn = still acute!

So: sometimes yes (if both turns are very small), but often no — two acute turns together can make a right angle or an obtuse angle.

Try opening each one at home or school and notice which way it turns:

Opening a tap: turn anti-clockwise (to the left) to let water flow.

Unscrewing a lid (like a bottle cap): turn anti-clockwise (to the left) to open.

Loosening a nut: turn anti-clockwise (to the left) to loosen.

This is a common rule: 'righty tighty, lefty loosey' — tighten by turning clockwise, loosen by turning anti-clockwise.

Compare each marked corner with a right angle (a square corner): smaller = acute, square = right, wider = obtuse.

A: wide, open corner of the roof peak = obtuse angle.

B: square corner where a wall meets the base = right angle.

C: narrow, sharp corner at the side of the roof = acute angle.

D: narrow, sharp corner at the lower edge = acute angle.

E: narrow, sharp corner at the side = acute angle.

F: square corner where two covers meet = right angle.

G: square corner at the base of the house = right angle.

H: wide corner of a tilted cover = obtuse angle.