128
Measuring angles in degrees
Textbook: Part 4, lesson 128, pp. 63–65
GoalMeasuring angles in degrees: 1° is 1/90 of a right angle; a right angle is 90°, a straight angle 180°, a full turn 360°.
New words
degree · gradusstraight angle · yoyiq burchakfull turn · to‘la aylanishunit of measure · o‘lchov birligi
Explanation
When angles cannot be laid on each other, we use a unit of measure. The unit for angles is the degree: 1/90 of a right angle, written 1°. A right angle is 90°, a straight angle 180° (two right angles) and a full turn 360° (four right angles). An acute angle is more than 0° and less than 90°; an obtuse angle is more than 90° and less than 180°. On a clock the minute hand turns 6° in 1 minute and the hour hand turns 30° in 1 hour.
Worked examples
At 4:00 the angle is 4 × 30 = 120° (obtuse).
A circle split into 8 equal sectors has 360 : 8 = 45° at the centre of each.
Class activity
“Angles with arms”: children show 90°, 180° and 45° angles with their arms; the teacher calls an angle and the others judge.
Practice
1
How many degrees does the minute hand turn in 15 minutes?
90
2
How many degrees is the angle between the hands at 4:00?
120
3
How many right angles make a straight angle?
2
4
How many degrees is half of a right angle?
45
5
A circle is split into 8 equal sectors. How many degrees is the angle at the centre of each sector?
45