Angles, lines and triangles

Revise Angles, lines and triangles for Mathematics A 4MA1 (O Level) — revision notes, 136 practice questions and instant AI marking.

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Pearson Edexcel International GCSE Mathematics A (4MA1)

Angles, lines and triangles

The big idea: Every angle question is a chain of small facts — angles on a line, parallel lines, the triangle sum — and each link in the chain needs its reason written next to it.

Summary — What This Chapter Covers

Name angles by size: acute (less than 90°), right (90°), obtuse (between 90° and 180°), reflex (between 180° and 360°).
Angles on a straight line add to 180°; angles at a point add to 360°; vertically opposite angles are equal.
With parallel lines: alternate angles are equal, corresponding angles are equal, allied (co-interior) angles add to 180°.
The angles in a triangle add to 180°; an exterior angle equals the sum of the two interior opposite angles.
Isosceles triangles have two equal sides and two equal base angles; equilateral triangles have three 60° angles.

1. Types of Angle

Foundation & Higher

Acute, right, obtuse, reflex

Name	Size
Acute	more than 0° and less than 90°
Right angle	exactly 90° (marked with a small square)
Obtuse	more than 90° and less than 180°
Straight line	exactly 180°
Reflex	more than 180° and less than 360°

An angle is named by three letters with the vertex in the middle: angle ABC (or ∠ABC) is the angle at B between BA and BC.

Practice Question 1

Write down the type of each angle: 95°, 205°, 18°, 179°.

2. Intersecting and Parallel Lines

Foundation & Higher

Five angle facts and their names

These are the facts the examiner wants to see quoted as reasons, in these words:

Angle facts Angles on a straight line add up to 180° · Angles at a point add up to 360° · Vertically opposite angles are equal

Parallel lines Alternate angles are equal (Z shape) · Corresponding angles are equal (F shape) · Allied (co-interior) angles add up to 180° (C shape)

Worked Example

A straight line crosses two parallel lines. Two allied angles between the parallel lines are (3x + 10)° and (2x − 5)°. Find the value of x and the size of each angle.

Practice Question 2

Three angles meet at a point. They are 2y°, 3y° and 140°. Find y.

3. Angles in a Triangle

Foundation & Higher

Angle sum and the exterior angle

The three interior angles of any triangle add up to 180°. If one side is extended, the exterior angle formed equals the sum of the two interior angles at the other two vertices (the interior opposite angles).

Triangle facts a + b + c = 180° exterior angle = sum of the two interior opposite angles

Worked Example

In triangle ABC, side BC is extended to D. Angle ACD = 125° and angle ABC = 48°. Find angle BAC and angle ACB.

4. Special Triangles

Foundation & Higher

Isosceles, equilateral and right-angled

Triangle	Sides	Angles
Equilateral	all three equal	all 60°
Isosceles	two equal (marked with dashes)	the two base angles, opposite the equal sides, are equal
Right-angled	longest side (hypotenuse) opposite the right angle

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Angles, lines and triangles