Discover Mathematics P4: Term 2, Unit 12, Lessons 6–10
GoalSort angles into acute, right, obtuse and straight by comparing them with a right angle, and draw them.
New words
acute angle · an angle smaller than a right angleobtuse angle · an angle larger than a right angle but smaller than a straight anglestraight angle · an angle whose arms make a straight line; two right angles together
Explanation
We sort angles by comparing them with a right angle. An acute angle is smaller than a right angle: it is less than 90°. A right angle is exactly 90°. An obtuse angle is larger than a right angle but smaller than a straight angle: it is more than 90° and less than 180°. A straight angle is exactly 180°, and its arms form a straight line. It is two right angles put together. To draw an angle, use a ruler: draw a ray, then draw a second ray from the same endpoint. The more the second ray opens away from the first, the larger the angle. Test your drawing with the corner of a paper to decide whether it is acute, right or obtuse.
Worked examples
Sort four angles. A opens less than a square corner, so it is acute. B fits the corner exactly, so it is right. C opens wider than a square corner but is not a straight line, so it is obtuse. D is a straight line, so it is a straight angle.
Time
1 o’clock
3 o’clock
4 o’clock
6 o’clock
Angle
acute
right
obtuse
straight
Sort by the hands of a clock. At 1 o’clock the hands make an acute angle. At 3 o’clock they make a right angle. At 4 o’clock they make an obtuse angle. At 6 o’clock they make a straight angle.
Draw an obtuse angle. Draw ray BA with a ruler. From B draw a second ray BC that opens wider than a square corner. Mark the opening with a small arc. Test: the paper corner fits inside the opening with room to spare, so the angle is obtuse.
Class activity
Angle cards. Draw twelve angles on separate cards: four acute, four obtuse, two right and two straight angles, but do not label them. Mix the cards. A friend uses the corner of a paper to sort them into four piles. Check the piles together and say how you know.
Practice
1
Name the type of each angle: A, B and C.
A is acute, B is obtuse and C is right.
2
A straight angle is made of how many right angles?
Two right angles: 90° + 90° = 180°.
3
Which angle is smaller than a right angle: acute, obtuse or straight?
An acute angle.
4
What type of angle do the hands of a clock make at 5 o’clock?
An obtuse angle: it is wider than a square corner but not a straight line.
5
Seif says a 100° angle is acute because it looks small. Is he right?
No. 100° is more than 90°, so it is wider than a right angle. It is obtuse.
