133
Drawing angles (practice)
Textbook: Part 4, lesson 133, pp. 78–79
GoalMore practice drawing angles: angle at the centre of a circle, drawing a triangle, halving an angle.
New words
central angle · markaziy burchakdrawing a triangle · uchburchak yasashhalving · teng ikkiga bo‘lishfull angle · to‘la burchak
Explanation
If two radii are drawn from the centre of a circle, the angle between them is a central angle. It can be written as a part of the full angle (360°): a 60° central angle is 60/360 = 1/6 of the full angle. To draw a triangle with two given angles, draw a base, draw those angles at its ends, and the point where the rays meet is the third vertex. To halve an angle, divide its measure by 2 and draw that angle.
Worked examples
A triangle with 40° and 70° at the ends of its base has third angle 180° − 40° − 70° = 70°.
Halving an 80° angle gives parts of 80 : 2 = 40°.
Class activity
“Circle clock”: children draw a cardboard circle, mark radii every 30° from the centre and say how many equal sectors there are (360 : 30 = 12).
Practice
1
What part of the full angle is a 40° angle at the centre of a circle?
1/9
2
Two angles of a triangle are 40° and 70°. How many degrees is the third?
70
3
An 80° angle is halved. How many degrees is each part?
40
4
One of two adjacent angles is 150°. How many degrees is the other?
30
5
Three sectors with central angles of 45° each are placed side by side. How many degrees is the total angle?
135