Lines & Angles on a Straight Line

Section 1 of 2

The Building Blocks

Points and lines

A point is a position, named with a capital letter ($A$, $B$). A line is straight and joins two points — line $AB$. A ray (half-line) $[AB$ starts at $A$ and goes on. A line segment $[AB]$ has two ends.

Distance

The distance from $A$ to $B$ is written $|AB|$. The two bars mean ‘the length of’.

Angles

Angles are measured in degrees with a protractor. A full circle is $360^\circ$. An angle is named by three letters with the corner in the middle: $\angle BAC$ (or just $\angle A$).

Section 2 of 2

Angles on a Straight Line

They add to 180°

Angles that sit on a straight line add up to $180^\circ$.

Worked example — find the missing angle

Find $A$.

$A + 150 = 180$

$A = 30^\circ$

Worked example — using x twice

On a straight line, three angles are $x$, $90^\circ$ and $x$. Find $x$.

$x + 90 + x = 180$

$2x + 90 = 180 \Rightarrow 2x = 90$

$x = 45$

You try

Two straight lines cross a line. On top, $2x$ and $150^\circ$ sit on a straight line; below, $3y$ and $150^\circ$ sit on a straight line. Find $x$ and $y$.

Each pair adds to $180^\circ$.

$2x + 150 = 180 \Rightarrow 2x = 30 \Rightarrow x = 15$

$3y + 150 = 180 \Rightarrow 3y = 30 \Rightarrow y = 10$

$x = 15,\ y = 10$

That’s Class 1.

Points, lines, naming angles, and angles on a straight line ($180^\circ$). Class 2: crossing lines and parallel lines.