angle measurement

In geometry an angle is the figure formed when two rays meet each other at a common endpoint called vertex.

∠AOB  is an angle with O as vertex and OA and OB as its arms.

Let’s now learn how to measure an angle. Roughly comparing the two angles we can say which angle is greater than the other. Like in figures below.

∠XYZ is wider open than ∠ABC , hence ∠XYZ> ∠ABC. But to know the exact measurement of angles, we use a tool known as ‘Protractor’.

A Protractor is a measuring instrument made of transparent plastic or glass. Protractor measures angles in degrees (°). It is the shape of a semicircle divided into 180 parts to measure and draw angles.

Place the midpoint of the protractor at the vertex of the angle, such that one side of the angle is in line with the protractor's zero line (a line that joins 0° and 180°) .

B is placed at the protractor midpoint and line BC is in line with the protractor zero line.

Line AB of ∠ABC   is crossing 60° in the number scale. Hence ∠ABC=60°

Let’s measure a few more angles. Both rays are in the same line and side. They make 0° angle.

Both rays are in the same line but on opposite sides to each other making an angle of 180°. Also called a straight angle.

Let’s use a protractor and measure the below angle.

∠ABC is 90°, also called a right angle. In other words, we can say AB is perpendicular to BC. \(AB \perp BC\).

Angles less than 90° are called acute angles. Angles greater than 90° are called obtuse angles. Let's use a protractor to measure the angle given in the below figure which is greater than 180°.

What is the measure of ∠CBD? Keeping the midpoint of the protractor at vertex B, measure ∠ABD, it is equal to 50°. Add 180 to 50, so the measure of ∠CBD=∠ABC+ ∠ABD=180°+ 50°=230°. 

An angle greater than 180° is called a reflex angle. 

A complete circle represents 360° angle.