It is very easy to calculate the third angle of a triangle when you know the measurements of the other two angles. To get the measure of the third angle, all you have to do is subtract the value of the other angles from 180 °. There are, however, other ways to calculate the measure of the third angle of a triangle, depending on the problem you are working on. If you want to know how to calculate the third angle of a triangle, read this guide.
Steps
Method 1 of 3: Using the Other Two Corners
Step 1. Add the two measurements of the known angles
Know that the sum of all angles of a triangle is always 180 °; it is a geometric rule that is valid always and in any case. Now, if you know two of the three measures of the triangle, you are only missing one piece of the puzzle. The first thing you can do is add up the angle measurements you know. In this example, the two known angle measurements are 80 ° and 65 °. Adding them (80 ° + 65 °) you get 145 °.
Step 2. Subtract the result from 180 °
The sum of the angles of a triangle is 180 °. Therefore, the remaining angle must necessarily have a value that, added to the two, gives as a result 180 °. In this example, 180 ° - 145 ° = 35 °.
Step 3. Write your answer
Now you know that the third angle measures 35 °. If in doubt, just check your calculation. The necessary condition for a triangle to exist is that the sum of its three angles is 180 °. 80 ° + 65 ° + 35 ° = 180 °. All done.
Method 2 of 3: Using Variables
Step 1. Write down the problem
Sometimes, instead of the measures of two angles of a triangle, you will be given only a few variables, or some variables and the measure of an angle. Let us assume that the problem is the following: Calculate the measure of the angle "x" of a triangle whose measures are "x", "2x" and 24. First, write down this data.
Step 2. Add all the measurements
It is the same principle that you would follow if you knew the measurements of the two angles. Just add the measurements of the angles, adding the variables. Hence, x + 2x + 24 ° = 3x + 24 °.
Step 3. Subtract the measurements from 180 °
Now, subtract these measurements from 180 ° to get to the solution of the problem. Make sure you make the equation equal to 0. Here's the process:
- 180 ° - (3x + 24 °) = 0
- 180 ° - 3x + 24 ° = 0
- 156 ° - 3x = 0
Step 4. Solve the unknown x
Now, write the variables on one side of the equation and the numbers on the other side. You will get 156 ° = 3x. Divide both sides of the equation by 3 to get x = 52 °. The measure of the third side of the triangle is 52 °. On the other hand, 2x equals 2 x 52 °, which is 104 °.
Step 5. Check your calculation
If you want to make sure the triangle is valid, just add the three angle measurements to make sure they give 180 °. That is, 52 ° + 104 ° + 24 ° = 180 °. All done.
Method 3 of 3: Using other Methods
Step 1. Calculate the third angle of an isosceles triangle
Isosceles triangles have two equal sides and two angles. Equal sides are both marked with an apostrophe, indicating that the angles of each side are equal. If you know the measure of one of the equilateral angles of an isosceles triangle, you can also know the measure of the angle of the opposite side. Here's how to calculate it:
If one of the equal angles is 40 °, then the other angle will also be 40 °. If necessary, you can calculate the third side by subtracting 40 ° + 40 ° (i.e. 80 °) from 180 °. 180 ° - 80 ° = 100 °; this is the measure of the remaining angle
Step 2. Calculate the third angle of an equilateral triangle
An equilateral triangle has all sides and angles equal. It will typically be marked with two apostrophes on each of the sides. This means that the measurement of any angle in an equilateral triangle equals 60 °. Check your calculation. 60 ° + 60 ° + 60 ° = 180 °.
Step 3. Find the third angle of a right triangle
Let's assume that your triangle is a right angle, with an angle of 30 °. If it's a right triangle, then you know that one of the corner measurements is exactly 90 degrees. The same principles apply. All you have to do is add the measurements of the known angles (30 ° + 90 ° = 120 °) and subtract the result from 180 °. So, 180 ° - 120 ° = 60 °. The measure of the third angle is 60 °.
