Week 29 · Drawing and composing angles · 3 lessons
3
Angle problems from real life
Discover Mathematics P4: Term 2, Unit 13, Lessons 9–12
GoalUse angle facts to solve real-life problems with doors, fans, wheels and clocks.
New words
equal angles · angles with the same sizetotal angle · the sum of the turns or angles added togetherturn · how far something rotates, measured in degrees
Explanation
Many real situations are angle problems. A door opening is a turn around its hinge: if it opens 40° and then 55° more, the total opening is 40° + 55° = 95°. Objects with equal parts around a centre, such as the blades of a fan or the cabins of a Ferris wheel, split a full turn of 360° into equal angles. Divide 360° by the number of parts: a fan with 4 equal blades has 360° ÷ 4 = 90° between blades. Clock hands turn too: the hour hand turns 30° each hour, so from 3 o’clock to 7 o’clock it turns 4 × 30° = 120°. First decide whether to add, subtract or divide. Draw a quick picture, write the number sentence, and check that your answer makes sense.
Worked examples
A ceiling fan has 4 equal blades. The angle between neighbouring blades is 360° ÷ 4 = 90°, a right angle. Check: 4 × 90° = 360°.
Menna opens a door by 40°, then pushes it 55° more. The total opening is 40° + 55° = 95°. This is a little more than a right angle, so the door is open as an obtuse angle.
From → to
1 → 5
2 → 8
3 → 4
Hours
4
6
1
Degrees
120°
180°
30°
The hour hand turns 30° each hour. From 1 o’clock to 5 o’clock it turns 4 hours: 4 × 30° = 120°. From 2 o’clock to 8 o’clock it turns 6 hours: 6 × 30° = 180°, half a full turn.
Class activity
Real angles. Find a fan, a pair of scissors, an open laptop or a door at home. Estimate the angle of its opening with the benchmarks 45°, 90° and 135°. Then measure with a protractor if you can. Write one story problem about an angle that opens by two stages (like the door) and solve it.
Practice
1
A garden gate opens 25° and then 30° more. What is the total opening?
25° + 30° = 55°.
2
A Ferris wheel has 12 cabins equally spaced round the centre. What is the angle between neighbouring cabins?
360° ÷ 12 = 30°.
3
A laptop screen is open 110°. Mina closes it by 35°. What is the new angle?
110° − 35° = 75°.
4
The hour hand moves from 2 o’clock to 8 o’clock. How many degrees does it turn?
From 2 to 8 is 6 hours: 6 × 30° = 180°.
5
Omar says a fan with 5 equal blades has 72° between neighbouring blades. Is he right?
