16.1 Angle facts at a point and on a line — Learn

Prerequisites: recognise a right angle and measure an angle in degrees. An angle measures a turn between two lines.

Objectives: use angles on a straight line, angles around a point, and vertically opposite angles. These are the G3 facts for this section.

Angles on lines and at points

Angles on a straight line add to $180^\circ$. Angles around a point add to $360^\circ$. Vertically opposite angles are the pair opposite each other where two straight lines cross; they are equal.

Example 1. A straight line is split into angles of $124^\circ$ and $x^\circ$. Find $x$.

The two angles make a straight turn, so their sum is $180^\circ$.

Example 2. Three angles around a point are $85^\circ$, $140^\circ$ and $y^\circ$. Find $y$.

The three angles complete one full turn.

Example 3. Two straight lines cross. One angle is $47^\circ$. Find the other three.

The opposite angle is $47^\circ$ because vertically opposite angles are equal. Each adjacent angle is $180-47=133^\circ$ because it lies on a straight line.

Watch out. The two angles next to $47^\circ$ are not equal to it. Each makes a straight line with it, so each is $133^\circ$. Check that opposite angles match.

Guided investigation: a full turn

Predict the missing angle when a full turn is split into $90^\circ$, $110^\circ$ and one unknown angle. Then use the figure to test your prediction. Explain how the angle sum checks your answer.

Progress check

The courtyard path is straight. If one tile edge makes $68^\circ$ with it, what is the adjacent angle? Name the fact you used.

You should now be able to

• use $180^\circ$ for angles on a straight line;
• use $360^\circ$ for angles around a point;
• find vertically opposite angles and state why they are equal.