# Types of Angles

> Name acute, right, obtuse, straight, reflex and revolution angles, and use angles on a line and around a point.

From Selective School Maths on WhizzNotes, free study notes for NSW students: https://whizznotes.com/selective-school-maths/classifying-angles/. Updated 3 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: The skateboard trick
At the skate park, Jordan's big sister talks in angles. "I did a three-sixty!" she shouts as she spins all the way round. Her friend lands a "one-eighty", turning to face the other way.

An **angle** measures how much something turns. A full spin is $360^\circ$, half a spin is $180^\circ$ and a quarter spin is $90^\circ$. Builders, pilots, sailors and skaters all use these numbers every day.

**In short:** Angles are named by their size: acute is less than $90^\circ$, right is exactly $90^\circ$, obtuse is between $90^\circ$ and $180^\circ$, and reflex is more than $180^\circ$. Angles on a straight line add to $180^\circ$ and angles around a point add to $360^\circ$.

## Before you start

- Angles are measured in **degrees**, written with a small circle: $90^\circ$.
- A **protractor** measures angles. You do not need one for this chapter.
- Adding and subtracting numbers up to 360.

## The six kinds of angle

*Diagram: Six angle types: acute, right, obtuse, straight, reflex and revolution*
*The arc shows which angle is meant. A small square marks a right angle.*

| Name | Size |
|---|---|
| **Acute** | less than $90^\circ$ |
| **Right** | exactly $90^\circ$ |
| **Obtuse** | between $90^\circ$ and $180^\circ$ |
| **Straight** | exactly $180^\circ$ |
| **Reflex** | between $180^\circ$ and $360^\circ$ |
| **Revolution** | exactly $360^\circ$ |

### Exam tip: Memory hooks
**Acute** sounds like "a cute little angle", so it is small. **Obtuse** is big and blunt. **Reflex** bends right back past a straight line.

### Watch out: Look at the arc
The same two arms make two angles: a small one and a reflex one. They add up to $360^\circ$. The arc in the diagram tells you which one the question wants. If the small angle is $40^\circ$, the reflex angle is $320^\circ$.

## Angles on a straight line

### Key idea: Straight line: $180^\circ$
Angles that sit together on a straight line add up to $180^\circ$.

If one is $130^\circ$, the other is $180^\circ - 130^\circ = 50^\circ$.

Two angles that add to $180^\circ$ are called **supplementary**. Two angles that add to $90^\circ$ are called **complementary**.

## Angles around a point

### Key idea: Around a point: $360^\circ$
Angles that go all the way around a point add up to $360^\circ$.

### Worked example: A right angle and a reflex angle
Around a point there is a reflex angle of $203^\circ$, a right angle and an angle $x$.

$x = 360 - 203 - 90 = 67$, so the angle is $67^\circ$.

### Worked example: Inside a right angle
A right angle is split into two parts. One part is $48^\circ$. The other part is $90^\circ - 48^\circ = 42^\circ$.

## Vertically opposite angles

When two straight lines cross, they make an X. The angles **opposite** each other are equal. These are called **vertically opposite** angles.

If one angle of the X is $70^\circ$, the angle across from it is $70^\circ$, and the other two are each $110^\circ$, because $70 + 110 = 180$.

### Challenge: Selective level: angles as fractions of a turn
A clock's minute hand turns $360^\circ$ in 60 minutes, so $6^\circ$ each minute. In 20 minutes it turns $120^\circ$.

At 3 o'clock the hands make a right angle, $90^\circ$. At 4 o'clock they make $4 \times 30^\circ = 120^\circ$, because each hour mark is $\frac{360}{12} = 30^\circ$ apart.

Three angles around a point are $x^\circ$, $2x^\circ$ and $3x^\circ$. Then $6x = 360$ and $x = 60$. The angles are $60^\circ$, $120^\circ$ and $180^\circ$.

**Mind map**

```text
Angles
  Small
    Acute: under 90°
    Right: 90°
  Medium
    Obtuse: 90° to 180°
    Straight: 180°
  Big
    Reflex: 180° to 360°
    Revolution: 360°
  Rules
    Straight line: 180°
    Around a point: 360°
    Vertically opposite: equal
```

## Quick summary

- Acute $< 90^\circ$, right $= 90^\circ$, obtuse between $90^\circ$ and $180^\circ$, straight $= 180^\circ$, reflex between $180^\circ$ and $360^\circ$, revolution $= 360^\circ$.
- Angles on a straight line add to $180^\circ$. They are supplementary.
- Angles that make a right angle add to $90^\circ$. They are complementary.
- Angles around a point add to $360^\circ$.
- Vertically opposite angles are equal.

## Quiz

Try these questions from the chapter quiz.

1. What type of angle is $135^\circ$?
   - A. acute
   - B. right
   - C. obtuse
   - D. reflex
   - Answer: C. obtuse. It is between $90^\circ$ and $180^\circ$.

2. What type of angle is $250^\circ$?
   - A. obtuse
   - B. straight
   - C. reflex
   - D. revolution
   - Answer: C. reflex. It is between $180^\circ$ and $360^\circ$.

3. Two angles on a straight line are $130^\circ$ and $x$. What is $x$?
   - A. $50^\circ$
   - B. $230^\circ$
   - C. $60^\circ$
   - D. $40^\circ$
   - Answer: A. $50^\circ$. $180 - 130 = 50$.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/selective-school-maths/classifying-angles/#quiz