11
Measuring angles. The protractor
Textbook: pp. 30–31
GoalMeasure angles in degrees and use a protractor.
New words
degree · gradusprotractor · transportirminute and second · minut va sekundangle measure · burchak o‘lchovi
Explanation
If a straight angle is divided into 180 equal angles, each part is 1 degree (1°). So a straight angle equals 180°. Every angle has a definite positive degree measure; equal angles have equal measures and vice versa. One 60th of a degree is a minute (1′), one 60th of a minute is a second (1″): 1° = 60′, 1′ = 60″. We find an angle’s measure with a protractor: put its centre on the vertex and its base along one side, then read the mark where the other side crosses the scale. Main property: if ray OC passes between the sides of ∠AOB, then ∠AOB = ∠AOC + ∠COB.
Worked examples
Ray OC lies inside ∠AOB, ∠AOC = 35°, ∠COB = 50°. Then ∠AOB = 35° + 50° = 85°.
If ∠AOB = 110° and ∠AOC = 70° (OC inside), then ∠COB = 110° − 70° = 40°.
Class activity
“Estimate and check”: first draw 30°, 60°, 90° and 120° angles by eye, then check with a protractor and note your error.
Practice
1
Ray OC lies inside ∠AOB, ∠AOC = 48°, ∠COB = 37°. Find ∠AOB (degrees).
85
2
∠AOB = 140°, OC inside, ∠AOC = 90°. Find ∠COB (degrees).
50
3
At 5:00 what is the angle between the hour and minute hands? (Each hour mark is 30°.)
150
4
Why must ray OC pass between the sides of ∠AOB for ∠AOB = ∠AOC + ∠COB to hold?
If OC lies outside, ∠AOC and ∠COB do not fill ∠AOB; they overlap or go beyond it.