An angle is a measure of the space between two lines that meet at a point. Angles are used in many fields, such as geometry, engineering, architecture, art, and photography. Knowing how to measure and draw angles can help you create accurate designs, solve problems, and express your creativity.
In this article, you will learn what an angle is, how to measure it using different tools, and how to draw it using a protractor or a compass. You will also learn about different types of angles, such as acute, right, obtuse, straight, reflex, and full angles.
What is an angle?
An angle is formed when two rays (or line segments) meet at a common endpoint called the vertex. The rays are called the sides of the angle. The size of an angle is measured in degrees (Â°), which are divided into 360 equal parts in a full circle. A full circle has 360Â°, a half circle has 180Â°, a quarter circle has 90Â°, and so on.
To name an angle, we use three letters: one for the vertex and one for each side. For example, in the figure below, the angle is called â ABC or â CBA. We can also use a number to label an angle, such as â 1.
How to measure an angle?
There are different tools that can help you measure an angle, such as a protractor, a ruler, a compass, or an online angle finder. Here are some steps to follow for each tool:
Using a protractor
A protractor is a semicircular device that has markings from 0Â° to 180Â°. To measure an angle with a protractor:
Place the center of the protractor on the vertex of the angle.
Align one side of the angle with the 0Â° mark on the protractor.
Read the number on the protractor where the other side of the angle intersects it. This is the measure of the angle in degrees.
For example, in the figure below, the measure of â ABC is 60Â°.
Using a ruler
A ruler can help you measure an angle if you know the length of the sides of the angle and use some trigonometry formulas. To measure an angle with a ruler:
Measure the length of the sides of the angle using the ruler. For example, if the sides are 5 cm and 7 cm long.
Use the cosine formula to find the measure of the angle: cos(â ABC) = (AB^2 + BC^2 – AC^2) / (2 Ã AB Ã BC), where AB, BC, and AC are the lengths of the sides. For example, cos(â ABC) = (5^2 + 7^2 – AC^2) / (2 Ã 5 Ã 7).
Solve for AC using the Pythagorean theorem: AC^2 = AB^2 + BC^2 – 2 Ã AB Ã BC Ã cos(â ABC). For example, AC^2 = 5^2 + 7^2 – 2 Ã 5 Ã 7 Ã cos(â ABC).
Plug in AC into the cosine formula and solve for â ABC using a calculator. For example, â ABC = cos^-1((5^2 + 7^2 – AC^2) / (2 Ã 5 Ã 7)) â 46.57Â°.
Using a compass
A compass is a tool that can help you draw circles and arcs. To measure an angle with a compass:
Draw an arc that intersects both sides of the angle using the compass