Special angles

Learn about special angles, like the right angle and the straight angle.

Vidya turns her book's cover in different ways. Holding the book to write, she turns the cover all the way round to the back: a full turn. Laying the book open flat on her table, she makes a half turn: the two arms now lie in a straight line. An angle that is a half turn is called a straight angle.

Take a straight angle ∠AOB. Any ray OC from O splits it into two angles, ∠AOC and ∠COB. Can the two be equal? Fold paper so that OB lies exactly on OA: the crease cuts the straight angle into two equal angles. Each of these is a right angle. So a straight angle contains two right angles.

A straight angle is half a full turn, so a right angle is half of a half turn: a quarter turn. It looks like the corner of the letter L, or the corner of a page. An angle is a right angle only if it is exactly half of a straight angle. Two lines that meet at a right angle are called perpendicular lines.

Other angles are sorted by comparing them with a right angle:

Acute angle: less than a right angle (less than a quarter turn). 'Acute' means sharp.
Obtuse angle: more than a right angle but less than a straight angle (more than a quarter turn, less than a half turn). 'Obtuse' means blunt.

A straight angle is a half turn with its arms in a straight line; a right angle is exactly half of it (a quarter turn, like an L); acute angles are less than a right angle and obtuse angles lie between a right angle and a straight angle.

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