Kinds of angle by measure

Sort angles into kinds by their size in degrees.

Each kind of angle can now be described in degrees:

Kind	Size
acute	more than 0°, less than 90° (like 40°, 50°, 75°)
right	exactly 90°
obtuse	more than 90°, less than 180° (like 110°)
straight	exactly 180°
reflex	more than 180°, less than 360°

Reflex angles are the new kind. Two arms from one vertex make two angles: the turn one way round, and the turn the other way round. Together they make a full turn, 360°. So if one is 100°, the reflex angle the other way round is 360° − 100° = 260°.

Known angles help find unknown ones. In your book, B, E and R lie on one straight line, with E between B and R, so ∠REB is a straight angle: 180°. A ray ES stands straight up from E, perpendicular to the line, so ∠SER = 90°. Another ray ET leans a little towards R, between ES and ER, with ∠TER = 80°.

Then:

∠BET is the rest of the straight angle: 180° − 80° = 100°.
∠SET is the small gap between ES and ET: the right angle ∠SER minus ∠TER, 90° − 80° = 10°.

Subtract from 180° (a straight line), 90° (a right angle) or 360° (a full turn).

Acute angles are between 0° and 90°, right 90°, obtuse between 90° and 180°, straight 180°, reflex between 180° and 360°; an unknown angle is found by subtracting from 180°, 90° or 360°.

Kinds of angle by measure.

Practise this lesson

Questions that get harder as you improve, a Tutor that helps without giving the answer away, and progress you can see. Free for every learner.

Try it now Sign up free I have an account

No account, no email address. Opens the real product.