☰ Year plan · Mathematics

Term 2 review

Week 30 · Term 2 review · 3 lessons
3

Review: angles and mixed problems

Discover Mathematics P4: Term 2, Units 9–13, Review
GoalReview angles, the clock face and the protractor, and solve mixed problems.
New words
acute, right, obtuse · smaller than 90°, exactly 90°, between 90° and 180°protractor · a half-circle tool to measure and draw angles from 0° to 180°full turn · 360°, all the way round
Explanation

Angles are sorted by comparing with a right angle: acute is less than 90°, right is 90°, obtuse is between 90° and 180°, and straight is 180°. A full turn is 360°, a half turn 180° and a quarter turn 90°. On a clock face each hour space is 360° ÷ 12 = 30°, so at 4 o’clock the angle between the hands is 4 × 30° = 120°. To measure with a protractor, estimate first, put the centre mark on the vertex and the baseline on one arm, then read the scale that starts at 0° on that arm. To draw an angle, draw a ray, place the protractor, mark the number, and join. Angles can be added: parts make the whole. Angles on a straight line add to 180° and angles round a point add to 360°. Subtract to find a missing angle, and check by adding.

Angleacuterightobtusestraightfull turn
Sizeless than 90°90°between 90° and 180°180°360°
Worked examples
18001701016020150301404013050120601107010080909080100701106012050130401403015020160101700180105°
Measure this angle. Estimate: it is wider than a square corner, so it is obtuse. The baseline is on the right arm, so read the scale that starts at 0° on the right: 105°. The other scale shows 75°, but that is less than 90°, so it does not match the estimate.
50°70°?O
Three angles lie on a straight line: 50°, 70° and a missing angle. A straight line is 180°. The missing angle is 180° − 50° − 70° = 60°. Check: 50° + 70° + 60° = 180°.
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At 5 o’clock the angle between the hands is 5 × 30° = 150°, which is obtuse. The hour hand then turns 3 more hours to 8 o’clock. It turns 3 × 30° = 90°, a quarter turn.
Class activity

Angle detective. Draw an angle of 65° and one of 115° with a protractor, next to each other on a straight line. Do they add up to 180°? Then set a toy clock to 2, 4 and 10 o’clock and write the angle between the hands each time. Finish by measuring two angles in your room.

Practice
1
Read the angle in the picture. The baseline is on the right arm.
18001701016020150301404013050120601107010080909080100701106012050130401403015020160101700180
2
Two angles lie on a straight line. One is 135°. Find the other.
3
A spinner is divided into 9 equal sections. What is the angle of each section?
4
Is an angle of 100° acute, right or obtuse?
5
What is the smaller angle between the hands of a clock at 10 o’clock?