Angles

How steep is a ramp? How far have you turned? Wherever two lines meet, an angle appears. Once you can measure and name angles, you understand shapes, maps and even the hands of a clock much better.

How an angle forms

An angle forms when two rays start from a shared point, the vertex. How far the two spread apart is measured in degrees, written with a small circle: 90°. A full turn around the circle is 360°, a half turn is 180°, and a quarter turn is exactly 90°. A clock face shows this directly: its twelve hour marks split the full 360° into twelve equal steps of 30° each.

Acute, right, obtuse

Angles are sorted by their size. An angle between 0° and 90° is called acute, exactly 90° is a right angle, often marked with a little square. Between 90° and 180° lies the obtuse angle. Exactly 180° is a straight angle, where the two rays form one straight line.

Vertical and adjacent angles

When two straight lines cross, four angles appear. The two that sit exactly opposite each other are called vertical angles and are always equal. Two angles that lie side by side and together form a straight line are called adjacent angles. They always add up to 180°. If one is 70°, the other is 110°.

Adding angles together

Angles that share a vertex and fit together without gaps can be added. All angles around a point together make 360°, all angles on a straight line together make 180°. This lets you find missing angles without measuring: if one of three around a point is missing and the others are 90° and 120°, then 360° − 90° − 120° = 150° is left.