A figure made of two rays from one point is called an angle; the point is the vertex and the rays are the sides. An angle is measured in degrees (°) with a protractor. A straight angle is 180° and its half, a right angle, is 90°. An angle less than 90° is acute; an angle greater than 90° and less than 180° is obtuse. If ray OC passes inside angle AOB, then ∠AOB = ∠AOC + ∠COB. A ray that divides an angle into two equal angles is called a bisector. When measuring, put the base line on one side and the centre at the vertex, then read the number shown by the other side. By measuring we can see that the angles of a triangle add up to 180°.
Worked examples
If ∠KLM = 76° and LN is its bisector, then ∠KLN = 76° : 2 = 38°. The bisector of a straight angle divides it into two angles of 180° : 2 = 90°.
If two angles of a triangle are 48° and 73°, the third is 180° − 48° − 73° = 59°. If ∠AOB = 84°, ∠AOC = 28° and ray OC is inside, then ∠COB = 84° − 28° = 56°.
Class activity
“Clock angles”: using a model clock, pupils turn the minute hand for 10, 20 and 30 minutes, say the angles (60°, 120°, 180°) and name their types. They fold paper to make an angle bisector.
Practice
1
A straight angle is split in two and one part is 34°. How many degrees is the other?
146
2
Into two angles of how many degrees does the bisector of a 150° angle split it?
75
3
Two angles of a triangle are 35° and 67°. Find the third angle.
78
4
Why does the bisector of a straight angle split it into two right angles?
A straight angle is 180° and the bisector halves it: 180° : 2 = 90°, a right angle.