# Straight Angle — Definition, Properties, and Examples

## TL;DR
A straight angle is an angle that measures exactly 180°, formed when its two arms point in opposite directions from a shared vertex and line up into a straight line. This article defines the straight angle, lists its properties, separates it from a straight line, and works through examples involving supplementary pairs and triangles.

A **straight angle** is an angle whose measure is exactly **180°**. Its two arms (the rays forming the angle) lie in opposite directions from the vertex, so together they make a straight line. In radians, a straight angle equals π. It is one entry in the wider family of types of angles, sitting between an obtuse angle (less than 180°) and a reflex angle (more than 180°).

A straight angle is also called a **flat angle**, and it represents exactly half of a full turn — since a complete revolution is 360°, and half of that is 180°.

## Properties of a Straight Angle
A handful of facts cover almost every straight-angle problem.

- **Measures exactly 180°.** No more, no less. An angle of 179° or 181° is not a straight angle.
- **Forms a straight line.** The two arms point in opposite directions, so the angle visually becomes a straight line through the vertex.
- **Equals two right angles.** A [right angle](/content/math/geometry/right-angle/index.html) is 90°, and 90° + 90° = 180°.
- **Equals half a full turn.** A full rotation is 360°; a straight angle is half of it, or \(\frac{360°}{2} = 180°\).
- **Equals π radians.** When angles are measured in radians, a straight angle is π.

## A Straight Angle is not the Same as a Straight Line
**Is a straight line the same as a straight angle?** No. A straight _line_ is a geometric object that extends forever in both directions and has no vertex. A straight _angle_ is a measurement of 180°, taken at a specific vertex where two arms meet. The arms of a straight angle happen to lie along a straight line, but the angle is the _amount of turn_ at the vertex, not the line itself.

Think of it this way: every straight angle traces out part of a straight line, but a straight line on its own carries no angle until you mark a vertex on it and look at the two directions leaving that point. The related [straight line](/content/math/geometry/straight-line/index.html) is the object; the straight angle is the 180° turn measured on it.

## Examples of Straight Angle
These move from recognizing the angle, through supplementary pairs, to a triangle's angle sum.

### Example 1
**The hands of a clock at 6:00 point straight up and straight down. What angle do they form?**

At 6:00 the minute hand points to 12 and the hour hand points to 6 — exactly opposite directions from the center.

**Final answer:** 180°, a straight angle.

### Example 2
**Two angles sit on a straight line and a student assumes they must each be 90°. Where does this go wrong?**

Test it. Angles on a straight line are **supplementary**, so they add to 180°, but they are not forced to be equal. If one is 120°, the other must be 60°, since 120° + 60° = 180°.

**Final answer:** They add to 180° but need not each be 90°.

### Example 3
**A straight angle is split into two parts. One part is 65°. Find the other.**

The two parts together form the straight angle, so they sum to 180°.

**Final answer:** 115°.

### Example 4
**How many right angles fit inside a straight angle?**

A right angle is 90° and a straight angle is 180°.

**Final answer:** Two right angles.

### Example 5
**A triangle has two angles measuring 40° and 75°. Use the straight-angle idea to find the third.**

**Final answer:** 65°.

### Example 6
**Two supplementary angles are in the ratio 2:3. Find both angles.**

**Final answer:** 72° and 108°.

## Why a Name For "Flat" is Useful
Naming 180° gives geometry a clean reference for "completely reversed direction," and that reference shows up far beyond worksheets.

## Mistakes With Straight Angles
### Mistake 1: Confusing a straight angle with a straight line
**Where it slips in:** When a figure shows a straight line and the reader is asked whether it is a straight angle.

### Mistake 2: Assuming angles on a straight line are always equal
**Where it slips in:** On linear-pair problems where one angle is given.

### Mistake 3: Mixing up a straight angle with a full angle
**Where it slips in:** When converting between halves and whole turns.

## Conclusion
- A **straight angle** measures exactly 180° and forms a straight line through its vertex.
- It equals two right angles, half a full turn, and π radians.
- A straight angle is a measurement at a vertex; a straight line is the object — they are not the same.
- Angles on a straight line are supplementary (sum to 180°) but need not be equal.
- A triangle's three interior angles always sum to a straight angle, 180°.