Angles

Different types of Angles

Angle: In Euclidean geometry, an angle is a figure formed by two rays with the same endpoint, denoted by “∠”.

Angles

 

In the figure, two rays OP and OQ make an angle ∠POQ at their common point O. O is vertex of the angle ∠POQ.

Right Angle: A right angle is an angle of exactly 90° (degrees). A 360-degree circle divided into 4 equal segments would contain 4 right angles.

Angles

 

AC is the common side of the angles ∠BAC and ∠DAC. If ∠BAC and ∠DAC are equal, then each of the two angles is right angle. The line segment AC and BD are mutually perpendicular. Mathematically denoted by AC⊥BD.

Acute Angle: An acute angle is smaller than 90 degrees.

Angles

 

In the figure, ∠AOC is an acute angle. Moreover, ∠AOB is a right angle.

Obtuse angle: An obtuse angle has a measurement greater than 90 degrees but less than 180 degrees.

Angles

 

In the figure, ∠AOD is an obtuse angle. Moreover, ∠AOB is a right angle.

 

Straight angle: A straight angle looks like a straight line and measures 180 degrees. If a circle is cut in half, the straight side of each semicircle will be a straight angle.

Angles

 

∠BAC is straight angle. The measurement of a straight angle is 2 right angles or 180 degree.

Reflex Angle: A reflex angle is greater than 180 degrees but less than 360 degrees.

Angles

 

∠AOC is a reflex angle.

Adjacent angles: Adjacent angles have a common vertex and one side of it is common.

Angles

 

The ∠BAC and ∠DAC have the same vertex A, common side AC and are on opposite sides of AC. ∠BAC and ∠DAC are adjacent angles.

Complementary angles: Two angles that are equal to 90 degrees when joined together are considered complementary.

Angles

The angles ∠AOC and ∠BOC are complementary angles.

Supplementary Angle: Two angles are called supplementary when their measures add up to 180 degrees.

Angles

The measurement of these two angles is equal to the measurement of the straight angle ∠AOB i.e., two right angles. The angles ∠AOC and ∠COB are supplementary angles.

Opposite Angle: Two angles are said to be the opposite angle if the sides of one are the opposite rays of the other.

Angles

The angles ∠BOD and ∠AOC as well as ∠BOC and ∠AOD are two pairs of opposite angles.

Interior and Exterior Angles: If a side of a triangle is produced, a new angle is formed. This angle is known as Exterior angle. Except the angle adjacent to the exterior angle, the two others angle of the triangle are known as opposite interior angles.

Angles

The angle ∠ACD is an exterior angle of the triangle ABC. ∠ABC, ∠BAC, ∠ACB are three interior angles.

Moreover, ∠ACD = ∠BAC + ∠ABC