Types of Angles

Angles are classified by their measure in degrees — acute, right, obtuse, straight, and reflex. Understanding angle types is the foundation of geometry.

What Is an Angle?

An angle is formed where two rays share a common endpoint (the vertex). Angles are measured in degrees (°).

From left to right: acute (< 90°), right (= 90°), and obtuse (> 90°).

Classifying Angles

Name	Range	Example
Acute	0° – 90°	45°
Right	exactly 90°	90°
Obtuse	90° – 180°	120°
Straight	exactly 180°	180°
Reflex	180° – 360°	270°

Complementary and Supplementary

Complementary Angles

\alpha + \beta = 90°

Two angles that together make a right angle.

Supplementary Angles

\alpha + \beta = 180°

Two angles that together make a straight line.

Tip Memory trick: Complementary = Corner (right angle, 90°). Supplementary = Straight line (180°).

If one angle is 35°, find its complement and supplement.

Complement: $90° - 35° = 55°$

Supplement: $180° - 35° = 145°$

Real world: clock hands

At 3 o'clock the minute and hour hands form a right angle (90°).

At 6 o'clock they form a straight angle (180°).

At 1 o'clock the angle is $\frac{1}{12} \times 360° = 30°$ — an acute angle.

Real world: wheelchair ramp angle

Building regulations require wheelchair ramps to have an incline no steeper than about 4.8° (a 1:12 ratio). This is a very small acute angle — ensuring safe, accessible passage for wheelchair users.

Real world: opening a laptop

A laptop screen swings from 0° (closed) to roughly 135° (fully tilted back). At around 90° the screen is upright — a right angle. Tilted further it passes through obtuse territory.

Practice Problems

Classify an angle of 112°.

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Obtuse (it is between 90° and 180°).

Two angles are supplementary. One measures 67°. What is the other?

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180° − 67° = 113°.