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

Calculate the size of angle X given that the triangle is equilateral.

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:

$x=60$

60

Below is an equilateral triangle.

Calculate X.

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:

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

$X=55$

55

ABC is an equilateral triangle.Calculate X.

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:

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

$7.5=x$

7.5

Tree angles have the sizes:

50°, 41°, and 81.

Is it possible that these angles are in a 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.

Impossible.

Tree angles have the sizes 56°, 89°, and 17°.

Is it possible that these angles are in a triangle?

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.

Impossible.

Tree angles have the sizes:

31°, 122°, and 85.

Is it possible that these angles are in a 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.

Impossible.

Three angles measure as follows: 60°, 50°, and 70°.

Is it possible that these are angles in a 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.

Possible.

Tree angles have the sizes 94°, 36.5°, and 49.5. Is it possible that these angles are in a 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.

Possible.

Tree angles have the sizes:

69°, 93°, and 81.

Is it possible that these angles are in a 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.

No.

Tree angles have the sizes:

90°, 60°, and 30.

Is it possible that these angles are in a 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.

No.

Tree angles have the sizes:

90°, 60°, and 40.

Is it possible that these angles are in a 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.

Yes.

Tree angles have the sizes:

76°, 52°, and 52°.

Is it possible that these angles are in a 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.

Yes.

Find the measure of the angle $\alpha$

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:

$\alpha=180-147$

$\alpha=33$

33

Find the measure of the angle $\alpha$

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

Therefore, we will use the formula:

$A+B+C=180$

We will substitute the known data:

$\alpha+27.7+41=180$

$\alpha+68.7=180$

We will move the term to the other side and maintain the appropriate sign:

$\alpha=180-68.7$

$\alpha=111.3$

111.3

Find the measure of the angle $\alpha$

Let's 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.

There is no possibility of resolving

Find all the angles of the isosceles triangle using the data in the figure.

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

62, 62, 56

Find all the angles of the isosceles triangle using the data in the figure.

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

70, 55, 55

Find all the angles of the isosceles triangle using the data in the figure.

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

90, 45, 45

Look at the isosceles right triangle below. What are its angles?

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

90, 45, 45

Find the measure of the angle $\alpha$

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:

$\alpha=180-100$

$\alpha=80$

80