Angles
Section: Geometry | Syllabus: Cambridge Primary Mathematics (0845)
Classifying, Estimating, Measuring and Drawing Angles
An angle measures the amount of turn between two lines meeting at a point. Angles can be classified by size, estimated by comparing them to familiar reference angles, and measured or drawn precisely using a protractor.
- Angles are classified by size:
- Acute - less than 90°
- Right angle - exactly 90°
- Obtuse - between 90° and 180°
- Straight - exactly 180°
- Reflex - between 180° and 360°
- Before measuring exactly, you can estimate an angle by comparing it to a right angle (90°) - is it clearly smaller, close to the same size, or clearly bigger?
- To measure an angle with a protractor:
- place the centre point exactly on the vertex
- line up one line with 0°
- then read off the value where the second line crosses the scale
- To draw an angle of a given size: draw a base line, place the protractor's centre point on one end with 0° lined up along the line, mark a point at the correct number of degrees, then join the vertex to that point
Always read from the 0° that lines up with the first line - the other scale gives the wrong angle
Worked Example: Measuring an Angle with a Protractor
- Question: A line is drawn from the 0° mark of a protractor to the 55° mark on the scale that starts at that line. What type of angle is this, and what is its size?
- Step 1: Read the value on the scale that starts at 0° along the first line: 55°
- Step 2: Compare 55° to 90° - it is smaller, so the angle is acute
- Answer: 55°, an acute angle
Common Mistakes
MistakeReading the wrong scale on a protractor - the two scales run in opposite directions, giving two different-looking numbers for the same line
Fixalways start counting from the 0° that lines up with the first line of the angle, not the 0° at the other end
Angles in a Triangle
The three interior angles of any triangle always add up to 180°, no matter the triangle's shape or size. This fact can be used to find a missing angle when the other two are known.
- The sum of the interior angles in any triangle is always 180°
- To find a missing angle, add the two known angles together, then subtract that total from 180°
The three angles of any triangle fit together to make a straight line - 180°
Worked Example: Finding a Missing Angle in a Triangle
- Question: A triangle has angles of 62° and 79°. What is the third angle?
- Step 1: Add the two known angles: 62 + 79 = 141
- Step 2: Subtract from 180: 180 − 141 = 39
- Answer: 39°
Common Mistakes
MistakeAdding all three angles together instead of subtracting from 180° to find the missing one
Fixadd only the two known angles first, then subtract that total from 180° to find the missing angle
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