Types of Triangles: Finding the size of angles in a triangle

Remember that the sum of angles in a triangle is equal to 180.

In an equilateral triangle, all sides and all angles are equal to each other.

Therefore, we will calculate as follows:

$x+x+x=180$

$3x=180$

We divide both sides by 3:

$x=60$

Since in an equilateral triangle all sides are equal and all angles are equal. It is also known that in a triangle the sum of angles is 180°, we can calculate X in the following way:

$X+5+X+5+X+5=180$

$3X+15=180$

$3X=180-15$

$3X=165$

Let's divide both sides by 3:

$\frac{3X}{3}=\frac{165}{3}$

$X=55$

Since this is an equilateral triangle, all angles are also equal.

As the sum of angles in a triangle is 180 degrees, each angle is equal to 60 degrees. (180:3=60)

From this, we can conclude that: $60=8x$

Let's divide both sides by 8:

$\frac{60}{8}=\frac{8x}{8}$

$7.5=x$

To determine which type of triangle we are dealing with, let's calculate angle alpha based on the fact that the sum of angles in a triangle is 180 degrees.

$\alpha=180-30-10=140$

Since alpha is equal to 140 degrees, the triangle is an obtuse triangle.

In an isosceles triangle, the base angles are equal to each other, meaning:

$B=C$

Since we are given angle A, we can calculate the base angles as follows:

Let's remember that the sum of angles in a triangle is equal to 180 degrees.

$180-50=130$

$130:2=65$

$B=C=65$

Since we are given that the triangle is isosceles, we will remember that the base angles are equal to each other.

That is:

$B=C=50$

Now we can calculate the vertex angle.

Since the sum of angles in a triangle is equal to 180 degrees, we will calculate the vertex angle as follows:

$A=180-50-50=80$

Therefore, the values of the angles in the triangle are: 80, 50, 50

Let's remember that in an isosceles triangle, the base angles are equal to each other.

In other words:

$C=B$

Since we are given the vertex angle, which is equal to 70 degrees, we'll recall that the sum of angles in a triangle is equal to 180 degrees.

Now let's find the base angles in the following way:

$180-70=110$

$110:2=55$

Therefore, the angle values in the triangle are: 55, 55, 70

In an isosceles triangle, we remember that the base angles are equal to each other, so angles C and B are equal to each other:

$C=B=62$

Now we can calculate the vertex angle.

We remember that the sum of angles in a triangle is equal to 180 degrees, therefore:

$A=180-62-62=56$

The angle values in the triangle are: 62, 62, 56

In the triangle shown in the diagram, we notice that one angle is a right angle equal to 90 degrees.

We'll remember that in an isosceles right triangle, the base angles are equal to each other.

Since the sum of angles in a triangle is equal to 180, we can calculate the angles as follows:

$180-90=90$

$90:2=45$

Therefore, the angle values in the triangle are: 90, 45, 45

Let's remember that the sum of angles in a triangle is equal to 180 degrees.

In a right triangle, there is one right angle equal to 90 degrees.

In an isosceles triangle, the base angles are equal to each other.

Therefore, we can calculate this in the following way:

$180-90=90$

$90:2=45$

In other words, the angle values in this triangle are: 90, 45, 45

Let's remember that the sum of angles in a triangle equals 180 degrees.

Let's calculate X in the following way:

$3x+5x+x=180$

$9x=180$

Let's divide both sides by 9:

$x=20$

Now let's calculate the angles:

$3x=3\times20=60$

$5x=5\times20=100$

This means that in the triangle we have 3 angles: 20, 60, 100

Since we have one angle that is greater than 90 degrees, meaning an obtuse angle, this is an obtuse triangle.

Let's remember that the sum of angles in a triangle equals 180 degrees.

Let's calculate alpha in the following way:

$60+\alpha+\frac{\alpha}{2}=180$

$60+1\frac{1}{2}\alpha=180$

$1\frac{1}{2}\alpha=180-60$

$1\frac{1}{2}\alpha=120$

Let's divide both sides by 1.5:

$\alpha=80$

Now we can calculate the remaining angle in the triangle:

$\frac{\alpha}{2}=\frac{80}{2}=40$

So in the triangle we have 3 angles: 60, 80, 40

All of them are less than 90 degrees, therefore all angles are acute angles and the triangle is an acute triangle.

Since we are given an angle of 45 and an angle of 90, we will refer to the triangle and calculate the missing angle based on the theorem that the sum of angles in a triangle equals 180 degrees.

Let's call this angle alpha:

$\alpha+45+90=180$

$\alpha+135=180$

Let's move the sides:

$\alpha=180-135$

$\alpha=45$

Looking at the second triangle, we notice that the angle adjacent to 90 will also be equal to 90 since it complements to 180 degrees.

Besides this, we don't have any more data, so we won't be able to calculate angles or determine the type of triangle.

To solve this exercise, we need to know two important laws-

In an equilateral triangle, all angles are equal as well.

The sum of angles in a triangle is 180.

Therefore, let's define the angle size as X.

We know that all angles are equal, and together they equal 180 degrees, so:

3X=180

Divide by 3

X=60

And thus we discovered that the angle size is 60 degrees!