Types of Angles

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

Angles on a straight line

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

Angles around a point

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 $70+110=180$.

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