Parts of a Triangle: 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.

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 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:

$50+41+81=172$

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.

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.

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:

$\alpha=180-147$

$\alpha=33$

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:

$\alpha=180-135$

$\alpha=45$

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 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:

$\alpha=180-68.7$

$\alpha=111.3$

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.

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 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:

$\alpha=180-94.5$

$\alpha=85.5$

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:

$\alpha+49.6+38=180$

$\alpha+87.6=180$

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

$\alpha=180-87.6$

$\alpha=92.4$

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:

$x=5$