Lines and Angles
Primary 4 · Mathematics
Lines and Angles
Lesson 5 of 5
25 min
Let's begin
Niyonzima is painting an imigongo pattern for the class wall. It is full of zigzags and points. "Some corners are sharp and some are wide," he says. "Do they have different names?"
Yes! Angles are sorted into kinds by their size. Once you know the kinds, you can name an angle just by looking at it.
| Kind | Size | Looks like |
|---|---|---|
| Acute | less than 90° | a sharp point, like the tip of an imigongo zigzag |
| Right | exactly 90° | a square corner |
| Obtuse | more than 90° but less than 180° | a wide-open corner, like a laptop lid pushed back |
| Straight | exactly 180° | a straight line |
| Reflex | more than 180° but less than 360° | the big angle on the outside of a corner |
A full turn of 360° takes you all the way round, back where you started.
Hold the corner of a sheet of paper against the angle. If the angle fits inside the paper corner, it is acute. If it fits exactly, it is right. If it is wider, it is obtuse.
A straight line makes 180°. If a ray splits the straight angle into two angles, the two angles add up to 180°.
Example: one angle on a straight line is 110°. The other angle is 180° − 110° = 70°.
In the same way, two angles that fill a right angle add up to 90°. If one is 35°, the other is 90° − 35° = 55°.
Tip
A-R-O-S-R, from small to big: Acute, Right, Obtuse, Straight, Reflex. Less than 90 is acute, 90 is right, between 90 and 180 is obtuse, 180 is straight, bigger than 180 is reflex.
Work each one in your exercise book first. Then tap Show answer to check.
What kind of angle is 45°?
Answer: Acute, because it is less than 90°.
What kind of angle is 160°?
Answer: Obtuse, because it is between 90° and 180°.
What kind of angle is 200°?
Answer: Reflex, because it is between 180° and 360°.
Two angles lie on a straight line. One is 125°. What is the other?
Answer: 55°, because 180 − 125 = 55.
The hands of a clock at 4 o'clock make 120°. What kind of angle is that?
Answer: Obtuse.
What you learned today
Sources and credits
Reflex angles are not in the Illustrative Mathematics lessons; that part was written by Ganzaa. The stories, Rwandan examples, diagrams and practice questions were written by Ganzaa.
Quick check
Match each angle to its kind.
Tap one on the left, then its partner on the right.
