Types of Angles in Math — Acute, Right, Obtuse, Straight, and Reflex

By MathPal Editorial Team·Published Apr 17, 2026

Grade: 6-7 | Topic: Geometry

What You Will Learn

An angle is formed when two rays share a common endpoint called the vertex. In this lesson you will learn to identify and classify the five main types of angles by their measure, understand how to read a protractor, and apply angle classification to solve problems.

Theory

What is an Angle?

When two rays extend from the same point, the amount of rotation between them is measured in degrees (symbol: °). A full turn around a point is $360°$, a half turn is $180°$, and a quarter turn is $90°$.

The Five Types of Angles

Type	Measure	Example
Acute	Greater than $0°$ and less than $90°$	$35°$, $60°$, $89°$
Right	Exactly $90°$	The corner of a square
Obtuse	Greater than $90°$ and less than $180°$	$120°$, $145°$, $179°$
Straight	Exactly $180°$	A straight line
Reflex	Greater than $180°$ and less than $360°$	$200°$, $270°$, $350°$

Key idea: Every pair of rays actually creates two angles — one that is $360°$ minus the other. When an angle is less than $180°$, its partner is a reflex angle. For example, if two rays form a $110°$ angle on one side, the angle on the other side is $360° - 110° = 250°$ (a reflex angle).

Right Angles in Everyday Life

Right angles appear everywhere: the corners of books, window frames, door edges, and floor tiles. In diagrams, a right angle is marked with a small square at the vertex rather than an arc. Recognizing right angles quickly is important because many geometry formulas (area of a rectangle, the Pythagorean theorem) rely on right angles being present.

Measuring Angles with a Protractor

A protractor is a semicircular tool marked from $0°$ to $180°$. Here is how to use one:

1. Position: Place the center mark of the protractor exactly on the vertex of the angle.
2. Align: Rotate the protractor so that the $0°$ line sits along one ray of the angle.
3. Read: Follow the other ray to where it crosses the degree scale and read the number.

Most protractors have two scales (inner and outer). Use whichever scale starts at $0°$ along the ray you aligned in step 2.

Measuring reflex angles: Since a standard protractor only goes to $180°$, measure the non-reflex part first, then subtract from $360°$. If the smaller angle is $140°$, the reflex angle is $360° - 140° = 220°$.

Worked Examples

Example 1: Classify the angle

An angle measures $72°$. What type is it?

Since $0° < 72° < 90°$, the angle is acute.

Example 2: Finding a reflex angle

Two rays form a $155°$ angle on one side. What is the reflex angle on the other side?

$360° - 155° = 205°$

The reflex angle is $205°$.

Example 3: Using angle types in a triangle

A triangle has angles of $52°$, $38°$, and $90°$. Classify each angle and identify the triangle type.

• $52°$ is acute (less than $90°$).
• $38°$ is acute (less than $90°$).
• $90°$ is a right angle.

Because the triangle contains a right angle, it is a right triangle.

Example 4: Clock angle problem

What type of angle do the hour and minute hands of a clock form at 3:00?

At 3:00, the minute hand points at 12 and the hour hand points at 3. Each hour mark represents $\frac{360°}{12} = 30°$. The hands are 3 hour marks apart:

$3 \times 30° = 90°$

The hands form a right angle at 3:00.

Common Mistakes

Mistake 1: Forgetting reflex angles exist

❌ "Two rays form a 250° angle? That is impossible — angles only go up to 180°."

✅ Angles can measure anywhere from $0°$ to $360°$. An angle greater than $180°$ and less than $360°$ is a reflex angle. It represents the larger rotation between two rays.

Mistake 2: Reading the wrong protractor scale

❌ A student aligns one ray with $0°$ on the inner scale but reads the other ray on the outer scale, getting $60°$ instead of $120°$.

✅ Always read from the same scale. If you aligned with the inner $0°$, read the other ray on the inner scale. A quick check: if the angle looks wider than a right angle, the measurement should be greater than $90°$.

Mistake 3: Confusing "right" with "straight"

❌ "A straight angle is 90° because a right angle is a straight corner."

✅ A right angle is $90°$. A straight angle is $180°$ and looks like a straight line. The word "straight" refers to the line shape, not to something being correct.

Practice Problems

1. Classify an angle that measures $167°$.

Show Answer

Since $90° < 167° < 180°$, the angle is obtuse.

2. The angle between two rays is $310°$. What type of angle is it? What is the non-reflex angle on the other side?

Show Answer

$310°$ is a reflex angle (between $180°$ and $360°$). The non-reflex angle is $360° - 310° = 50°$, which is acute.

3. At what time do clock hands form a straight angle?

Show Answer

At 6:00, the minute hand points to 12 and the hour hand points to 6. They are 6 hour marks apart: $6 \times 30° = 180°$, which is a straight angle.

4. A triangle has two angles of $45°$ and $45°$. Find the third angle and classify all three.

Show Answer

Third angle: $180° - 45° - 45° = 90°$. The two $45°$ angles are acute and the third is a right angle. This is an isosceles right triangle.

5. You measure the non-reflex side of an angle and get $85°$. What is the reflex angle? Classify both.

Show Answer

The non-reflex angle of $85°$ is acute. The reflex angle is $360° - 85° = 275°$, which is a reflex angle.

Summary

• An angle measures the rotation between two rays sharing a vertex.
• Acute angles are less than $90°$; right angles are exactly $90°$; obtuse angles are between $90°$ and $180°$.
• A straight angle is exactly $180°$; a reflex angle is between $180°$ and $360°$.
• Use a protractor by aligning its center on the vertex and its baseline along one ray, then reading the scale.
• For reflex angles, measure the non-reflex angle and subtract from $360°$.

Related Topics

• Angles in a Triangle — apply angle classification to find missing triangle angles.
• Area and Perimeter — right angles are fundamental to rectangle and square area formulas.
• Complementary and Supplementary Angles — learn how angle pairs add to $90°$ or $180°$.

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