Circles and types of angles | Sainik, Navodaya and RMS Coaching

There are seven types of Angles commonly used in Mathematics:

Zero Angle (0° in Measure)
Acute Angle (0 to 90° in Measure)
Right Angle (90° in Measure)
Obtuse Angle (90 to 180° in Measure)
Straight Angle (180° in Measure)
Reflex Angle (180 to 360° in Measure)
Complete Angle (360° in Measure)

Below is an explanation of each of the different types of angles with their figures:

Zero Angle: The two rays of the angle make zero degrees inclination w.r.t. each other i.e. the rays overlap. Here, Angle AOB denotes zero degrees in measure.

Zero Angle

Acute Angle: The two rays of the angle make zero to nighty degrees inclination. Here, Angle AOB denotes Acute degrees in measure.

Acute Angle

Right Angle: The two rays of the angle make 90 degrees inclination. Here, Angle AOB denotes 90 degrees in measure.

Right Angle

Obtuse Angle: The two rays of the angle make ninety to one-hundred eighty degrees inclination. Here, Angle AOB denotes Obtuse degrees in measure.

Obtuse Angle

Straight Angle: The two rays of the angle make one-hundred eighty degrees inclination or the rays are straight line w.r.t to each other. Here, Angle AOB denotes 180 degrees in measure

Straight Angle

Reflex Angle: The two rays of the angle make one-hundred-eighty to three hundred sixty degrees inclination. Here, Angle AOB denotes Reflex angle in measure.

Reflex Angle

Complete Angle: The two rays of the angle make three hundred sixty degrees inclination. Here, Angle AOB denotes Complete angle in measure.

Complete Angle

Sample Problems

Question 1: An Angle A measures 135° in measure. Which type of category does Angle A fall into?

Answer:

Angle A lies between 90° to 180° in measure. Angle A is, therefore, an Obtuse Angle.

Question 2: An Angle S measures 35° in measure. Which type of category Angle S falls into?

Answer:

Angle S lies between 0° to 90° in measure. Angle S is therefore an Acute Angle.

Question 3: An Angle X measures 235 degrees in measure. Which type of category Angle X falls into?

Answer:

Angle X lies between 180° to 360° in measure. Angle X is therefore a Reflex Angle.

Question 4: An Angle Z measures 335° in measure. Which type of category does Angle Z fall into?

Answer:

Angle Z lies between 180° to 360° in measure. Angle Z is therefore a Reflex Angle.

Types of Angle Pairs

A pair of angles denotes two angles. Let us read about the various angle pairs in geometry.
Adjacent Angles

For two angles to be adjacent angles, the following conditions should be true.

Two angles share a common vertex.
Two angles share a common arm.
There are two arms that are not common.

Adjacent Angles
Complementary Angles

When the sum of two angles is equal to 90°, they are called complementary angles. The two angles can be of any measure such that they sum up to 90°. For example, the two angles can be 30° and 60°. Here, one angle is the complement of the other angle.
Supplementary Angles

When the sum of two angles is equal to 180°, they are called supplementary angles. The two angles when added make up 180°. For example, 110° and 70° make up 180°. So these two angles are said to be supplementary. Here, one angle is the supplement of another angle. For example, the supplement of 60° is (180° - 60°), which is 120°.
Alternate Interior Angles

When a line or a transversal passes through two parallel lines the angles formed at the opposite sides of the line or the transversal are called alternate interior angles which are equal.
Alternate Exterior Angles

When a line or a transversal passes through two parallel lines the angles that are formed at the external side of the line or transversal are called alternate exterior angles which are equal.
Corresponding Angles

When a line or a transversal passes through two parallel lines the angles that are formed at the same position or on the same side of the transversal are corresponding angles and these angles are congruent.
Vertical Angles

When two lines intersect each other, the angles opposite to each other are equal and are termed as vertical angles, or, vertically opposite angles.

Observe the following figure to relate to the angles given above.

Alternate, Corresponding and Vertical Angles