# Different Types of Angles with Formulas and Examples

If you ever get a chance to look around you there are so many Types of Angles that you might notice. Moreover, from a closed door to a sharpened pencil to our Earth’s axis, they all have Angles. However, differentiating between all of them might seem like a task. But in this blog, you will learn about all the 15 Types of Angles along with their formulas as well as examples to help you differentiate.

## Acute Angle

An Acute angle is an angle that measures less than 90 degrees.

The Formula for an Acute angle is: Acute Angle = x°, where 0° < x < 90°

Example: An angle of 45 degrees is an Acute angle or the corner of a sharpened pencil.

## Right Angle

A Right angle is an angle that measures exactly 90 degrees.

The Formula for a Right angle is: Right Angle = 90°

Example: The angle formed by the intersection of two perpendicular lines is a Right angle or a closed door.

Here the Right Angle is ABC and AGD.

## Obtuse Angle

An Obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees.

The Formula for an Obtuse angle is: Obtuse Angle = x°, where 90° < x < 180°

Example: An angle of 135 degrees is an Obtuse angle or a leaning tree.

## Straight Angle

A Straight angle is an angle that measures exactly 180 degrees.

The Formula for a Straight angle is: Straight Angle = 180°

Example: The angle formed by a line segment that extends in a Straight line is a straight angle.

## Reflex Angle

A Reflex angle is an angle that measures more than 180 degrees but less than 360 degrees.

The Formula for a Reflex angle is: Reflex Angle = x°, where 180° < x < 360°

Example: An angle of 225 degrees is a Reflex angle or the hands of a clock forming a “V” shape.

## Full Rotation Angle

A Full Rotation angle is an angle that measures exactly 360 degrees.

The Formula for a Full Rotation angle is: Full Rotation Angle = 360°

Example: The angle formed by a complete revolution around a circle is a Full Rotation angle or the Earth’s rotation on its axis.

## Positive Angles

Positive angles are angles that are measured in a counterclockwise direction from the positive x-axis.

The Formula for a Positive angle is: Positive Angle = x°, where 0° ≤ x < 360°

Example: An angle of 45 degrees measured in a counterclockwise direction from the positive x-axis is a Positive angle. Moreover, any Acute, Obtuse, or Reflex angle.

## Negative Angles

Negative angles are angles that are measured in a clockwise direction from the positive x-axis.

The Formula for a Negative angle is: Negative Angle = -x°, where -360° < x ≤ 0°

Example: An angle of -45 degrees measured in a clockwise direction from the positive x-axis is a Negative angle.

Adjacent angles are two angles that share a common vertex and a common side. The sum of the measures of Adjacent angles is always 180 degrees.

The Formula for Adjacent angles is: Adjacent Angles = x° + y°, where x° + y° = 180°

Example: The two angles formed by the intersection of two perpendicular lines are Adjacent angles.

## Complementary Angles

Complementary angles are two angles whose sum is exactly 90 degrees.

The Formula for Complementary angles is: Complementary Angles = x° + y°, where x° + y° = 90°

Example: An angle of 25 degrees and an angle of 65 degrees are Complementary angles or two Acute angles on a perpendicular line.

## Supplementary Angles

Supplementary angles are two angles whose sum is exactly 180 degrees.

The Formula for Supplementary angles is: Supplementary Angles = x° + y°, where x° + y° = 180°

Example: An angle of 120 degrees and an angle of 60 degrees are Supplementary angles or two Straight angles next to each other.

## Alternate Interior Angles

Alternate Interior angles are two angles that are on opposite sides of a transversal line and are on the interior of the two parallel lines.

The Formula for Alternate Interior angles is: Alternate Interior Angles = x°, where x° = y°

Example: The angles formed by a transversal line intersecting two parallel lines are Alternate Interior angles.

## Alternate Exterior Angles

Alternate Exterior angles are two angles that are on opposite sides of a transversal line and are on the exterior of the two parallel lines.

The Formula for Alternate Exterior angles is: Alternate Exterior Angles = x°, where x° = y°

Example: The angles formed by a transversal line intersecting two parallel lines, but on the exterior of the parallel lines, are Alternate Exterior angles.

Here AGE and DOF are Alternate exterior angles.

## Corresponding Angles

Corresponding angles are two angles that are on the same side of a transversal line and are on the same side of the two parallel lines.

The Formula for Corresponding angles is: Corresponding Angles = x°, where x° = y°

Example: The angles formed by a transversal line intersecting two parallel lines, where the angles are on the same side of the transversal line, are Corresponding angles.

## Vertical Angles

Vertical angles are two angles that are opposite each other when two lines intersect.

The Formula for Vertical angles is: Vertical Angles = x°, where x° = y°

Example: The angles formed by the intersection of two lines are Vertical angles.

## Maths Problems on Angles with Solutions

1. An angle measures 120 degrees. What type of angle is it?
Answer: Obtuse angle (An obtuse angle has a measure greater than 90° but less than 180°).
2. Line m intersects line n at point O. If angle 1 measures 45 degrees, what is the measure of its complementary angle?
Answer: 45 degrees (Since they are complementary, the other angle must also measure 45 degrees to reach 90 degrees).
3. Two rays, OA and OB, lie on a straight line. What is the measure of angle AOB?
Answer: 180 degrees (A straight line creates an angle of 180 degrees).
4. The angles in a triangle add up to 180 degrees. If one angle in a triangle measures 60 degrees and another measures 70 degrees, what type of angle is the third angle?
Answer: Acute angle (The third angle must be less than 50 degrees (180 – 60 – 70) to fit within the triangle).
5. At what time on an analog clock do the hour and minute hands form a right angle (90 degrees)?
Answer: 3:00 (The hour hand moves 360 degrees in 12 hours, so it moves 30 degrees every hour.)