Module 5 of 6 · MA4-ANG-C-01
Unknown angles
Use given information to find the sizes of unknown angles
01
Every line of working needs a reason
The test says 'give reasons'. A correct number with no reason loses marks. Write the reason in brackets after each line: x = 74° (vertically opposite angles).
02
Angles at a point
Angles on a straight line add to 180°. Angles all the way around a point add to 360°. A right angle is 90°. Complementary angles add to 90°; supplementary angles add to 180°.
03
Work in steps
You often can't get from what you know to what you want in one jump. Find an angle you *can* get, write it on the diagram, and use it as the stepping stone to the next one.
04
Mark the diagram as you go
Write every angle you work out onto the figure. It costs five seconds and it turns an invisible chain of reasoning into something you can see.
The rules to know by heart
- Angles on a straight lineadd to 180°
- Angles at a pointadd to 360°
- Vertically opposite anglesare equal
- Complementary anglesadd to 90°
- Supplementary anglesadd to 180°
See it work
Try it — the answer is given, you name the rule
0 / 0 correct39° + x = 180° — why?
A worked example
Find the size of angle x, and give the reason.
Worked solution
- 43° + x = 180°(angles on a straight line add to 180°)
Every line has its reason in brackets. In the test, that bracket is worth marks on its own — write it even when the number feels obvious.
Words for this module
Acute angle
An angle smaller than 90°.
Right angle
Exactly 90°, marked on a diagram with a small square.
Obtuse angle
An angle between 90° and 180°.
Straight angle
Exactly 180° — a straight line.
Reflex angle
An angle between 180° and 360°.
Watch out: To find a reflex angle, work out the small angle first and subtract from 360°.
Revolution
A full turn — 360°. Angles at a point add to one revolution.
Complementary angles
Two angles that add to 90°.
Watch out: C comes before S in the alphabet, and 90 before 180: Complementary = 90°, Supplementary = 180°.
Supplementary angles
Two angles that add to 180°.
Vertically opposite angles
The equal angles formed opposite each other when two lines cross (the X shape).
Watch out: These are equal whether or not any lines are parallel.
Adjacent angles
Two angles that share a vertex and an arm, and don't overlap.
ready?
Practise until you get five in a row.