Lines and Angles

Points, lines, line segments and rays, the kinds of angles, turns and directions, and the angles made by the hands of a clock.

Key ideas

A line goes on forever both ways; a line segment has two end points; a ray has one end point and goes on forever the other way.
An angle is made by two rays from the same point (the vertex); its size is how much one arm turns to reach the other.
A full turn is 360°, a half turn 180° and a quarter turn 90°.
Acute: less than 90°. Right: 90°. Obtuse: between 90° and 180°. Straight: 180°. Reflex: more than 180°.
North, East, South and West are a quarter turn (90°) apart.

Remember

Hour hand	30° for every hour; ½° for every minute
Minute hand	6° for every minute; one full turn every hour
Turns	¼ turn = 90°; ½ turn = 180°; full turn = 360°

Watch out

Reading the wrong scale on a protractor (start from the 0 on the arm).
Thinking the hour hand stays still while the minutes pass.
Calling a 180° angle obtuse (it is a straight angle).

Worked example

School starts at 7 o'clock in the morning and ends 4 hours later. Through how many degrees does the hour hand turn during the school day, and through how many full turns does the minute hand go?

Working: 4 × 30° = 120°; the minute hand makes one full turn every hour (ends at 11 o'clock)

Answer: 120°; 4 full turns