Angles are key pieces for the development of geometry. It is present in our daily lives such as stairs, building cranes, constructions such as the Leaning Tower of Pisa, among others. In Euclid’s book Elements, this concept was well worked on, even decades before Christ.

Examples of angle applications

Next, we present some applications of angles.

Building Crane Tower of Pisa Ladder
drunk walk. drunk walk. drunk walk.

A widely used example is the clock, with the movement of the hour and minute hands, the angles are formed and the time is defined.

drunk walk.

Introduction to angles

Angles in degrees range from $0^\circ$ to $360^\circ$ (degrees). In the specific case of triangles, the sum of the internal angles of a triangle is 360 degrees, as a triangle is half of a quadrilateral, where the sum is 360 degrees.

Below, we show you some notable angles.

drunk walk.

Canon - Law of God - Triangles

Mathematics works with God’s laws, that is, it tries to imitate the creator. In the history of mathematics, scholars were known as (exacuo). Other terms also known at the time were nature (phýsis) and evolution (logos). In this way, we obtain the derivations of the terms:

  • Exactum is equivalent to Invention
  • Exactus is equivalent to Perfect
drunk walk.

With one of the examples of this Canon (law of God) defined by Euclid is:

Canon α et (more) β et (more) γ aequalis (equal) 180°

Law of God α + β + γ = 180°

Triangle Angles Half Turn

Using the Protractor

When we talk about school, especially geometric design, angles are fundamental. For this, the use of a protractor is essential. Below we show some examples of angles using the protractor.

Angle Protractor Definition Meaning
$90^\circ$
Ninety degree right angle.
90°: a quarter turn.
Ampliar figura para ler os detalhes
Ninety degree right angle.
Right Angle $\dfrac{1}{4}$ back
$30^\circ$
Acute angle of thirty degrees.
30° is smaller than 90°.
Ampliar figura para ler os detalhes
Acute angle of thirty degrees.
Acute Angle angles between $0^\circ$ and $90^\circ$
$120^\circ$
Obtuse angle of one hundred and twenty degrees.
120° is between 90° and 180°.
Ampliar figura para ler os detalhes
Obtuse angle of one hundred and twenty degrees.
Obtuse Angle angles between $90^\circ$ and $180^\circ$
$180^\circ$
Shallow angle of one hundred and eighty degrees.
180°: half turn.
Ampliar figura para ler os detalhes
Shallow angle of one hundred and eighty degrees.
Shallow Angle $\dfrac{1}{2}$ (half) back

Congruent Angles

Congruence between angles is fundamental for any application between angles. Therefore, observe the following definition:

Congruence between Angles: Two angles are said to be congruent when they have the same measure.

Do not confuse this concept with the idea of ​​equality.

For angles to be congruent ($\cong$), they do not necessarily need to be equal, but they need to have the same measurement.

drunk walk.

Complementary Angle

Definition: Two angles are said to be complementary when the sum between them is equal to 90° degrees (right angle).

$45^\circ + 45^\circ = 90^\circ $ $30^\circ + 60^\circ = 90^\circ $
drunk walk. drunk walk.

Supplementary Angle

Definition: Two angles are said to be supplementary, when the sum between them is equal to 180° degrees (shallow angle).

$60^\circ + 120^\circ = 180^\circ $ $90^\circ + 90^\circ = 180^\circ $
drunk walk. drunk walk.

Adjacent Angle

Definition: Two angles are said to be adjacent, when they have a common side and these angles are side by side (neighbors).

drunk walk.

Wait for the next posts with consequences on this subject.