☰ Year plan · Mathematics

Drawing and composing angles

Week 29 · Drawing and composing angles · 3 lessons
2

Putting angles together and taking them apart

Discover Mathematics P4: Term 2, Unit 13, Lessons 9–12
GoalAdd the parts of an angle to find the whole angle, and subtract a part to find the missing part.
New words
compose · to put angles together to make a bigger angledecompose · to break an angle into smaller anglesmissing angle · an angle whose size we do not know yet, found by subtracting
Explanation

Angles can be put together and taken apart. When two angles share a vertex and an arm and do not overlap, the whole angle is the sum of the parts. If angle ABD is 35° and angle DBC is 50°, then angle ABC is 35° + 50° = 85°. To find a missing part, subtract the known part from the whole: if the whole angle is 120° and one part is 45°, the other part is 120° − 45° = 75°. Two special wholes help us. A straight angle is 180°, so the angles on a straight line add up to 180°. A full turn is 360°, so all the angles around a point add up to 360°. After subtracting, check by adding the parts back to see if you get the whole.

35°50°O
Worked examples
35°50°O
Compose angles. Angle AOB is 35° and angle BOC is 50°. They share the arm OB. The whole angle AOC is 35° + 50° = 85°.
45°?O
Find a missing part. The whole angle AOC is 120° and the part AOB is 45°. The missing part BOC is 120° − 45° = 75°. Check: 45° + 75° = 120°.
65°?O
Angles on a straight line. The line AC is straight, so the angles on it add up to 180°. Angle AOB is 65°. The other angle BOC is 180° − 65° = 115°. Check: 65° + 115° = 180°.
Class activity

Paper angles. Cut a 90° corner from paper. Cut it into two pieces with a straight cut from the corner. Measure one piece with a protractor, say 35°, and work out the other: 90° − 35° = 55°. Measure it to check. Do this three times with different cuts. What is the sum of the two pieces each time?

Practice
1
Angle ABD is 40° and angle DBC is 30°. How big is angle ABC?
2
A right angle is split into two angles. One is 35°. How big is the other?
3
Two angles lie on a straight line. One is 120°. What is the other?
4
Three angles meet at a point. Two of them are 100° and 120°. What is the third?
5
Karim says 30° + 45° = 85°. Is he right?