What are the types of angles in geometry

The angle is one of the important concepts in geometry. An angle is formed when two lines intersect, or by a ray rotating around a fixed endpoint (common vertex). The ray is called the initial arm or the beginning side of the angle. The other side of the angle is called the terminal arm, or terminal side. Angles appear in variety of geometrical shapes, triangle, polygons, circles, etc. Understanding the types of angles is the beginning of deep dive of more complex angle related questions.

How is angle measured

The classification of the types of angles is based on the size of the angle. So first let's have a discussion of angles measurement.


An angle could be measured in two different ways, in degree or radian. In degree measurement, 1 degree is the size of angle that is equal to 1/360 of a central angle of a full circle. You can measure an angle in degrees ( °), using a protractor. In radians measurement, a central angle is an angle whose vertex is at the center of a circle. A central angle of 360° has a radian measure of 2 \pi . That is:


360° = 2\pi radians


If you divide both sides by 360, you will obtain the relationship between degrees and radians.


1 ° = \dfrac{1}{360} radian


How are angles classified


The size of an angle is determined by the inclination between two arms, rather than the length of the two arms. The angles could be classified as 10 types of angles based on their sizes and the direction of measurement, acute angle, right angle, obtuse angle, straight angle, reflex angle, non-reflex angle, round angle, negative angle, positive angle, zero angle.

Acute angle

An acute angle is an angle that is less than 90 degrees and larger than 0 degree. If all the three interior angles of a triangle are acute angles, this triangle is called acute angle triangle. The right hand side is a acute angle triangle with three angles less than 90 degrees.

Right angle

A right angle is an angle of exactly 90°. It is formed when two perpendicular straight lines intersect. If one angle of a triangle is right angle, the triangle is right triangle. in a right triangle, the sum of the other two angles is always 90 degrees.

Obtuse angle

An obtuse angle is an angle larger than 90° and smaller than 180°. In a triangle, there's only one angle could be obtuse angle as the sum of three angles of a triangle could not be larger than 180°. The difference between 180° and an obtuse angle must be an acute angle.

Straight angle

When the arms of an angle lie in the opposite direction, they form a straight angle. A straight angle is angle of 180°, which is also called flat angle.

Reflex angle

A reflex angle is an angle larger than 180° and less than 360°. In a circle, a central angle may divide a circle into two arcs. The larger of the two arcs is called the major arc. The central angle corresponding to the major arc is reflex angle.

Non-reflex angle

A non-reflex angle is on the opposite the smaller one of two central angles divided by the two arms of the angle in a circle. The arc corresponding to the non-reflex angle is called minor arc. A non reflex angle is less than 180° and larger than 0°. Acute angle, obtuse angle and right angle are all non-reflex angles.

Round angle

A round angle is an angle of 360° or 2π in radian. A central angle of a full circle is a round angle.

Negative angle

A negative angle is an angle that is measured in a clockwise direction.

Positive angle

A positive angle is, on the contrary, an angle that is measured in a counter clockwise direction.

Zero angle

A zero angle is an angle formed when both the angle's arms coincide at the same position.

Steven Zheng Steven Zheng posted 4 months ago

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