Parts of a Triangle: Finding the size of angles in a triangle

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:

$\alpha=180-147$

$\alpha=33$

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:

$\alpha+69+23=180$

$\alpha+92=180$

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.

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:

$\alpha=180-135$

$\alpha=45$

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 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.

First let's remember 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:

$\alpha=180-68.7$

$\alpha=111.3$

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.

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.

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'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 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:

$90+60+30=180$

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.

We can calculate BD according to the following rule:

In a right triangle, the midpoint of the hypotenuse is equal to half of the hypotenuse.

That is:

BD is equal to half of AC:

Given that: $AC=10$

$BD=10:2=5$

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

Therefore, we will use the following formula:

$A+B+C=180$

We'll substitute the known data:

$115+8x+20+x=180$

We'll combine similar terms:

$9x+135=180$

We'll move terms to one side and maintain the appropriate sign:

$9x=180-135$

$9x=45$

We'll divide both sides by 9:

$x=5$

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

Therefore, we will use the following formula:

$A+B+C=180$

Let's input the known data:

$11x+40x+80-x=180$

We'll combine the x terms:

$50x+80=180$

We'll move terms to one side and maintain the appropriate sign:

$50x=180-80$

$50x=100$

We'll divide both sides by 50:

$x=2$

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:

$89+5\frac{1}{2}+\alpha=180$

$\alpha+94.5=180$

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

$\alpha=180-94.5$

$\alpha=85.5$