130
Measuring angles with a protractor (practice)
Textbook: Part 4, lesson 130, pp. 69–71
GoalMore practice with the protractor: sum of adjacent angles, angles of a triangle.
New words
adjacent angles · qo‘shni burchaklarsum of angles · burchaklar yig‘indisitriangle · uchburchakstraight angle · yoyiq burchak
Explanation
When a ray splits a straight angle into two angles, the sum of their degree measures is always 180°. If we measure all three angles of a triangle and add, the sum comes out as 180° (measuring errors may change it by a degree or two). From this we can find an unknown angle: if two angles are known, the third = 180° − first − second.
Worked examples
A straight angle is split into 115° and ?: ? = 180° − 115° = 65°.
If two angles of a triangle are 62° and 48°, the third is 180° − 62° − 48° = 70°.
Class activity
“Three angles on a line”: children draw a triangle on paper and colour its three angles differently. They tear off the corners by hand (no scissors) and place them side by side with the vertices at one point. They see that together the angles make a straight angle (180°).
Practice
1
A ray splits a straight angle in two and one angle is 115°. How many degrees is the other?
65
2
A ray splits a straight angle into two angles, one twice the other. How many degrees is the smaller?
60
3
A ray splits a right angle in two and the first part is 30°. How many degrees is the second?
60
4
Two angles of a triangle are 62° and 48°. How many degrees is the third?
70
5
What sum do the angles of a triangle give?
180