Angles: parts, units and types, measuring with a protractor
Mathematics Prep 1 Term 1, Unit 4, Lessons 1–2
GoalName the parts of an angle, tell its type and measure it with a protractor.
New words
angle · two rays that start at the same pointvertex · the point where the two sides of an angle meetdegree · the unit for angles; a full turn is 360°reflex angle · an angle bigger than 180° and smaller than 360°
Explanation
An angle is formed by two rays, called its sides, that start at one point, the vertex. We write ∠ABC, with the vertex B in the middle, and m(∠ABC) for its measure in degrees. A full turn is 360°. (Each degree can be split into 60 minutes, but we will not need that.) The types are: zero angle 0°, acute (between 0° and 90°), right 90°, obtuse (between 90° and 180°), straight 180° and reflex (between 180° and 360°). A reflex angle equals 360° minus the angle on the other side. To measure with a protractor, put its centre on the vertex, put the 0 on one side, and read the scale that starts at 0 on that side.
Worked examples
Naming. The angle with vertex B and sides BA and BC is written ∠ABC. In the figure m(∠ABC) = 50°. The vertex letter always goes in the middle.
Types. 30° is acute because it is less than 90°. 90° is right. 130° is obtuse because it is between 90° and 180°. 250° is reflex because it is more than 180°.
Reading a protractor. One side lies on the 0 of the lower scale, so we read the same scale at the other side: 65°. The other scale shows 115°, but the angle is clearly smaller than a right angle. A reflex angle of 250° leaves 360° − 250° = 110° on the other side.
Class activity
Angle hunt. With a grown-up, look around the room for angles: a door opening, scissors, a book corner, a clock. Sort ten angles into acute, right, obtuse and straight. Open a book to make a right angle and use it to check.
Practice
1
Name the type of each angle: 75°, 90°, 160°, 270°.
75° acute, 90° right, 160° obtuse, 270° reflex.
2
An angle measures 110°. What is the reflex angle on the other side?
360° − 110° = 250°.
3
Read the angle on the protractor.
65°. The side is on the 0 at the right, so read the scale that starts with 0 there.
4
How big is a straight angle, and what does it look like?
180°. Its two sides form a straight line.
5
Youssef reads 115° for an acute angle on a protractor. What did he do wrong?
He read the wrong scale. An acute angle is less than 90°, so the right reading is 180° − 115° = 65°.
