Sheet № 150 · Foundation + Higher · AQA · Edexcel · OCR
Angles on a Straight Line and at a Point –
Angles on a straight line and at a point are the most fundamental angle facts in GCSE Maths. These rules underpin almost every geometry question across AQA, Edexcel, and OCR, so you must know them inside out. This guide covers the three key rules — angles on a straight line, angles at a point, and vertically opposite angles — with worked
§Key definitions
Question:
Three angles on a straight line are 65°, 48°, and x°. Find x.
Answer:
x = 33.3° (1 d.p.)
Q1 (Foundation):
Two angles on a straight line are 74° and x°. Find x.
Q2 (Foundation):
Three angles meet at a point: 150°, 95°, and y°. Find y.
Q3 (Higher):
Two straight lines cross. One angle is (4a + 10)° and the angle adjacent to it on the straight line is (2a + 50)°. Find a and all four angles.
§Formulas to memorise
Angles on a straight line add up to 180°
Angles at a point add up to 360°
Vertically opposite angles are equal
Identify the type of angle arrangement. — Decide whether the angles lie on a straight line, meet at a point, or are vertically opposite.
Write an equation. — Add all the angles together and set the total equal to 180° (straight line) or 360° (point).
Solve for the unknown. — Rearrange the equation and calculate the missing angle.
Check your answer. — Add all angles to confirm they reach the correct total.
Worked example
Three angles on a straight line are 65°, 48°, and x°. Find x.
Working:
⚠ Common mistakes
- ✗Confusing 180° and 360° rules. Angles on a straight line total 180°, not 360°. Angles at a point total 360°. Read the diagram carefully before choosing the rule.
- ✗Forgetting vertically opposite angles are equal. Students sometimes try to add vertically opposite angles together instead of setting them equal.
- ✗Not stating reasons. Exam questions often require you to give a reason — writing "angles on a straight line" is essential for method marks.
✦ Exam tips
- →Always write the angle rule you are using as a reason alongside your calculation.
- →If a diagram shows two crossing lines, immediately mark both pairs of vertically opposite angles as equal.
- →When multiple rules are needed in one question, apply them one at a time and show each step clearly.
- →These angle facts are often the first step in a multi-part geometry question, so getting them right is critical.