Sheet № 54 · Foundation + Higher · AQA · Edexcel · OCR
Angles: Basic Rules & Parallel Lines –
Angle rules and parallel line properties are among the most frequently tested topics in GCSE Maths. Whether you are taking Foundation or Higher tier with AQA, Edexcel, or OCR, you will encounter questions that ask you to find missing angles using basic rules such as angles on a straight line, angles around a point, and vertically opposite
§Key definitions
Question:
Two angles on a straight line are 3x° and (2x + 30)°. Find the value of x and both angles.
Answer:
x = 30, and both angles are 90°.
Question 1:
Angle A and angle B are on a straight line. Angle A = 127°. Find angle B.
Question 2:
Three angles meet at a point. Two of them are 145° and 85°. Find the third angle.
Question 3:
Two straight lines cross. One of the angles formed is 62°. Find all four angles.
§Formulas to memorise
Angles on a straight line — add up to 180°.
Angles around a point — add up to 360°.
Vertically opposite angles — are equal. When two straight lines cross, the angles opposite each other are the same.
Angles in a triangle — add up to 180°.
Angles in a quadrilateral — add up to 360°.
Alternate angles — (also called Z-angles) — angles on opposite sides of the transversal, between the parallel lines. They are equal.
Corresponding angles — (also called F-angles) — angles in matching positions at each intersection. They are equal.
Co-interior angles — (also called allied angles or C-angles) — angles on the same side of the transversal, between the parallel lines. They add up to 180°.
Read the question — and identify which angle you need to find.
Mark any parallel lines — look for arrow markings on the diagram.
Worked example
Two angles on a straight line are 3x° and (2x + 30)°. Find the value of x and both angles.
Working:
⚠ Common mistakes
- ✗Not giving reasons. Calculating the correct angle but writing no reason will cost you marks. Always name the rule.
- ✗Confusing alternate and corresponding angles. Alternate angles form a Z shape; corresponding angles form an F shape. Trace the shape on the diagram to be sure.
- ✗Assuming lines are parallel without evidence. Only use parallel line rules when the diagram states or shows (with arrows) that lines are parallel.
- ✗Adding co-interior angles instead of recognising they sum to 180°. Some students treat co-interior angles as equal — they are not. They are supplementary.
- ✗Mixing up interior and exterior angles. Interior angles are between the parallel lines; exterior angles are outside them.
✦ Exam tips
- →Write the angle fact in words next to each calculation, e.g. "Angles on a straight line sum to 180°." This earns the reason mark.
- →Mark angles on the diagram as you find them. This helps you spot further relationships.
- →Use algebra confidently. Foundation and Higher papers both include questions where angles are expressed as algebraic expressions. Set up the equation using the angle rule, then solve.
- →Look for multi-step problems. You may need to use one rule to find an intermediate angle and then a different rule to find the target angle. Plan your route through the problem.
- →If a question says "Give reasons for your answer", you must state a reason for every step — not just the final answer.