Angles
3.0 Geometry · 3.2 Angles
Syllabus tag: Kenya CBC | Grade 6 Mathematics | Strand 3.0 Geometry | Sub-Strand 3.2 Angles (6 Lessons)
Lesson objectives
By the end of this topic, you will be able to:
- Identify and measure angles on a straight line
- Work out the sum of angles on a straight line
- Determine the sum of angles in rectangles and triangles
- Construct equilateral, right-angled, and isosceles triangles
- Measure the interior angles of these triangles
- Appreciate the use of angles in real life
Angles
An angle measures turning. We measure it in degrees, written with a small circle like this: 90°.
a) Angles on a straight line
A straight line is half a full turn.
The angles along one side of a straight line always add up to 180°.
So if one angle is 120°, the other must be 60°. That is because 120 + 60 = 180.
b) Measuring an angle
Use a protractor.
Put its centre exactly on the corner of the angle. Line up the zero with one arm.
Read where the other arm crosses the scale. Use the scale that starts at zero on your arm. The other scale gives the wrong number.
Check your answer looks right. An angle smaller than a corner of a page is less than 90°.
c) Angle sums
The angles in any triangle add to 180°.
The angles in any rectangle add to 360°. Each corner is 90°, and there are four of them.
A full turn is 360°.
d) Finding a missing angle
Add the angles you know. Then take that total from the sum for that shape.
For a triangle, take from 180. For a rectangle, take from 360.
Always check by adding all the angles at the end. They should give the right total.
e) Three special triangles
An equilateral triangle has three equal sides and three equal angles. Each angle is 60°, because 180 ÷ 3 is 60.
A right-angled triangle has one angle of exactly 90°. The other two must add to 90.
An isosceles triangle has two equal sides, and the two angles opposite them are equal too.
f) Constructing them
For an equilateral triangle, draw the base. Set the compasses to the base length. Draw an arc from each end. Join the base ends to where the arcs cross.
For a right-angled triangle, construct a perpendicular first. Mark the two side lengths along the arms, then join.
For an isosceles triangle, draw the base. Set the compasses to the equal side length. Draw an arc from each end of the base, and join to where they cross.
Measure the angles afterwards with a protractor to check.
g) Where this is used
A carpenter cuts a corner. A builder checks a wall is upright. A designer sets out a pattern. A footballer judges a shooting angle.
Words to know
- Angle — the amount of turn between two lines that meet at a point, measured in degrees (°).
- Equilateral triangle — a triangle with all three sides and all three angles equal (each 60°).
- Isosceles triangle — a triangle with exactly two equal sides and two equal angles.
- Right-angled triangle — a triangle with one angle equal to exactly 90°.
- Interior angle — an angle inside a shape, at one of its corners.
:::checkpoint Check yourself
- What do angles on a straight line add up to?
- What do the angles of a triangle add up to?
- Two angles of a triangle are 40° and 75°. Find the third.
- What is each angle of an equilateral triangle? :::
Bridge to practice
Try the exercises below — finding missing angles on a line, in triangles, and in rectangles, using the two key facts above.