What is the answer to the triangle sum theorem?

Answer: The sum of the three angles of a triangle is always 180 degrees . To find the measure of the third angle, find the sum of the other two angles and subtract that sum from 180.

What is the triangle sum theorem 9th grade?

The sum of the interior angles in a triangle is supplementary. In other words, the sum of the measure of the interior angles of a triangle equals 180°. So, the formula of the triangle sum theorem can be written as, for a triangle ABC, we have ∠A + ∠B + ∠C = 180°.

What is the triangle theorem explanation?

The Triangle Inequality Theorem states: The difference between any two sides will be less than the third since the sum of any two sides is bigger than the third. The sum of any two sides is always greater than the sum of the 3rd side. The longest side in a triangle is the side opposite a greater angle.

What can you conclude about the triangle sum theorem?

One thing is for certain for all types of triangles: the measures of the three interior angles add up to 180 degrees. The Triangle Angle Sum Theorem states that the sum of all three interior angles of any triangle will always be 180 degrees .

What is the formula for the sum of a triangle?

This property states that the sum of all the interior angles of a triangle is 180°. If the triangle is ∆ABC, the angle sum property formula is ∠A+∠B+∠C = 180°.

How do you explain the theorem?

A theorem can be defined as a statement that can be proved to be true based on known and proved facts ; all theorems contain a math rule and at least one proof. The Pythagorean theorem states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the sides of the triangle.

What is the famous triangle theorem?

Pythagorean theorem , the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a 2 + b 2 = c 2 .

What is the full explanation of triangle?

A triangle is a polygon with three sides having three vertices . The angle formed inside the triangle is equal to 180 degrees. It means that the sum of the interior angles of a triangle is equal to 180°. It is a polygon having the least number of sides.

What is the sum of the angles of a triangle answer?

The sum of three angles in a triangle is 180° .

What is the sum theorem for triangular numbers?

There is a familiar formula to calculate a triangular number. It is the formula for the sum of the first n consecutive integers. It is n(n+1)/2 , and it is easy to derive it from the Subtraction Abacus.

What is the total theorem of triangle?

Theorem 1: The sum of all the three interior angles of a triangle is 180 degrees . Theorem 2: The base angles of an isosceles triangle are congruent. The angles opposite to equal sides of an isosceles triangle are also equal in measure.

Triangle Sum Theorem – Explanation & Examples (2024)

We know that different triangles have different angles and side lengths, but one thing is fixed — that each triangle is composed of three interior angles and three sides that can be of the same length or different lengths.

For instance, a right triangle has one angle that is exactly 90 degrees and two acute angles.

Isosceles triangles have two equal angles and two equal side lengths. Equilateral triangles have the same angles and same side lengths. Scalene triangles have different angles and different side lengths.

Even though all of these triangles differ in angles or side lengths, they all follow the same rules and properties.

In this article, you’ll learn about:

The Triangle Sum Theorem,
Interior angles of a triangle, and
How to use the Triangle Sum Theorem to find the interior angles of a triangle?

What is the Interior Angle of a Triangle?

In geometry, the interior angles of a triangle are the angles that are formed inside a triangle.

Interior angles have the following properties:

The sum of interior angles is 180 degrees (Triangle Angle Sum Theorem).
All interior angles of a triangle are more than 0° but less than 180°.
The bisectors of all three interior angles intersect inside a triangle at a point called the in-center, which is the center of the in-circle of the triangle.
The sum of each interior angle and exterior angle is equal to 180° (straight line).

What is the Triangle Angle Sum Theorem?

One common property about triangles is that all three interior angles add up to 180 degrees. This now brings us to an important theorem in geometry known as Triangle Angle Sum Theorem.

According to the Triangle Angle Sum Theorem, the sum of the three interior angles in a triangle is always 180°.

We can this as:

∠a + ∠b + ∠c = 180°

How to Find the Interior Angles of a Triangle?

When two interior angles of a triangle are known, it is possible to determine the third angle using the Triangle Angle Sum Theorem. To find the third unknown angle of a triangle, subtract the sum of the two known angles from 180 degrees.

Let’s take a look at a few example problems:

Example 1

Triangle ABC is such that, ∠A = 38° and ∠B = 134°. Calculate ∠C.

Solution

By Triangle Angle Sum Theorem, we have;

∠A + ∠B + ∠C = 180°

⇒ 38° + 134° + ∠Z = 180°

⇒ 172° + ∠C = 180°

Subtract both sides by 172°

⇒ 172° –172° + ∠C = 180° – 172°

Therefore, ∠C = 8°

Example 2