Sum and Difference of Angles: Finding the size of angles in a triangle

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.

Recall that the sum of angles in a triangle equals 180 degrees.

Therefore, we will use the following formula:

$A+B+C=180$

Now let's insert the known data:

$\alpha+50+50=180$

$\alpha+100=180$

We will simplify the expression and keep the appropriate sign:

$\alpha=180-100$

$\alpha=80$

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:

$\alpha=180-147$

$\alpha=33$

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:

$80+55+\alpha=180$

$135+\alpha=180$

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

$\alpha=180-135$

$\alpha=45$

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:

$\alpha+69+23=180$

$\alpha+92=180$

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

$\alpha=180-92$

$\alpha=88$

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

Therefore, we can use the formula:

$A+B+C=180$

Then we will substitute in the known data:

$\alpha+27.7+41=180$

$\alpha+68.7=180$

Finally, we will move the variable to the other side while maintaining the appropriate sign:

$\alpha=180-68.7$

$\alpha=111.3$

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

Therefore, we will use the formula:

$A+B+C=180$

Let's input the known data:

$100+\alpha+90=180$

$190+\alpha=180$

$\alpha=180-190$

We should note that it's not possible to get a negative result, and therefore there is no solution.

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.

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:

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

$7.5=x$

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:

$x=60$

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 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.

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:

$94+36.5+49.5=180$

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

Recall that the sum of angles in a triangle equals 180 degrees.

Let's add the three angles to see if their sum equals 180:

$60+50+70=180$

Therefore, it is possible that these are the values of angles in some triangle.

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 know that the triangle is isosceles, we know that the base angles are equal.

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 are 80, 50, and 50.