Angles
An angle measures the amount of turn between two lines that meet at a point, measured in degrees. Angle facts are fixed rules, like angles on a straight line adding to 180 degrees, that let you work out missing angles without measuring.
Before you start
No specific prerequisites - this is a good place to start.
Method
- Angles on a straight line add up to 180 degrees.
- Angles around a point add up to 360 degrees.
- Angles in a triangle add up to 180 degrees; angles in a quadrilateral add up to 360 degrees.
- Vertically opposite angles, formed when two lines cross, are always equal.
- Identify which angle fact applies to the diagram, write an equation using it, then solve for the missing angle.
Worked example
Two angles lie on a straight line. One is 3x degrees and the other is (x + 40) degrees. Find x and the size of each angle.
- Angles on a straight line sum to 180 degrees, so 3x + (x + 40) = 180.
- Simplify the left-hand side: 4x + 40 = 180.
- Subtract 40 from both sides: 4x = 140.
- Divide by 4: x = 35.
- The angles are 3(35) = 105 degrees and 35 + 40 = 75 degrees.
- Check: 105 + 75 = 180, which confirms the answer.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE exam paper, with a full mark scheme.
Two angles on a straight line are (2x + 15) degrees and (3x - 10) degrees. Work out the size of each angle.
A triangle has angles of (x + 10) degrees, (x + 10) degrees and (2x + 20) degrees. Show that the triangle is isosceles and find each angle.
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