Sum and Difference of Angles: 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:

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

$7.5=x$

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.

$180-50=130$

$130:2=65$

$B=C=65$

In an isosceles triangle, the base angles are equal to each other—that is, angles C and B are equal.

$C=B=62$

Now we can calculate the vertex angle.

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

$A=180-62-62=56$

The values of the angles in the triangle are 62, 62, and 56.

It is known that the sum of angles in a triangle is 180 degrees.

Since we are given two angles, we can calculate $a$

$94+92=186$

We should note that the sum of the two given angles is greater than 180 degrees.

Therefore, there is no solution possible.

Let's calculate the sum of the angles to see what total we get in this triangle:

$56+89+17=162$

The sum of angles in a triangle is 180 degrees, so this sum is not possible.

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

In other words:

$C=B$

We know the vertex angle, which is equal to 70 degrees, and we know that the sum of angles in a triangle is equal to 180 degrees.

Therefore, we can calculate the base angles in the following way:

$180-70=110$

$110:2=55$

Therefore, the angle values in the triangle are 55, 55, and 70.

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

In a right-angled 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, and 45.

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

Therefore, we will use the following formula:

$A+B+C=180$

Now let's input the known data:

$120+27+\alpha=180$

$147+\alpha=180$

We'll move the term to the other side and keep the appropriate sign:

$\alpha=180-147$

$\alpha=33$

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

Therefore, we will use the following formula:

$A+B+C=180$

Now let's input the known data:

$\alpha+69+23=180$

$\alpha+92=180$

We'll move the term to the other side and keep the appropriate sign:

$\alpha=180-92$

$\alpha=88$

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

We'll add the three angles to see if their sum equals 180:

$31+122+85=238$

Therefore, these cannot be the values of angles in any triangle.

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

We'll add the three angles to see if their sum equals 180:

$50+41+81=172$

Therefore, these cannot be the values of angles in any triangle.

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

We'll add the three angles to see if their sum equals 180:

$69+81+93=243$

Therefore, these cannot be the values of angles in any triangle.

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

We'll add the three angles to see if their sum equals 180:

$90+60+30=180$

Therefore, these could be the values of angles in some triangle.

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

We'll add the three angles to see if their sum equals 180:

$90+60+40=190$

Therefore, these cannot be the values of angles in any triangle.

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

We'll add the three angles to see if their sum equals 180:

$94+36.5+49.5=180$

Therefore, these could be the values of angles in some triangle.

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

We will add the three angles to find out if their sum equals 180:

$76+52+52=180$

Therefore, these could be the values of angles in some triangle.

Note 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.

Note 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

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