Geometry

Measuring and drawing angles

We measure angles in degrees (°).

There are 90° in a right angle.

 There are two right angles in a straight line.

A straight line is 180°.

 90° + 90° = 180°

A complete circle is the same as four right angles or 360°

90° + 90° + 90° + 90° = 360°

We can say that \(1\over 360\) th part of complete circle is equal to one degree.

An angle less than 90° is an acute angle.

An angle greater than 90° but smaller than 180° is an obtuse angle

Look at the angle ∠ABC.

We can use a protractor to measure the angle.

A protractor has a centre mark, an upper scale and a lower scale.

Look at the angle ∠ABC. Upper scale reads the measure of angles from left to right.

Lower scale reads the measure of angles from right to left.

Each small marking on the scales shows 1 degree ( 1° ).

To measure ∠ABC, place the protractor on the line BC such that the vertex is at the centre mark of the protractor. If the line lies on the 0° of the lower scale, we read the lower scale of the protractor. If the line lies on the 0° of the upper scale, we read the upper scale of the protractor.

\(\overrightarrow {BC }\) lies on the 0 of the lower scale,

 So, we will read the lower scale.

\(\overrightarrow {BA} \) falls on the marking that is 2 after 45.

So, ∠ABC measures 47 degrees.

We can also write it as ∠ABC = 47°

Measure the following:

We can also draw angles using a protractor

Let's draw m∠ABC = 30°