What is an angle?

An angle is the figure formed by two rays sharing a common endpoint, called the vertex. We measure how "open" an angle is in degrees — a full rotation is $360°$.

The four classes

| Type | Range | | --- | --- | | Acute | $0° < \theta < 90°$ | | Right | $\theta = 90°$ | | Obtuse | $90° < \theta < 180°$ | | Straight | $\theta = 180°$ |

Naming convention

We name an angle either by its vertex letter alone (∠B) or with three letters where the middle letter is the vertex (∠ABC — vertex at B).

Mnemonic: "Middle = vertex." If the middle letter changes, the angle changes.

Worked example

If two angles share a side and together form a straight line, they are supplementary: $\alpha + \beta = 180°$.

Given $\alpha = 47°$, find $\beta$:

$$\beta = 180° - 47° = 133°$$

Common trap

Students often confuse supplementary (sum to $180°$) with complementary (sum to $90°$). The letter "S" of "Straight" matches "Supplementary" — both are $180°$.