# 3.5 Exterior Angle Theorem and Triangle Sum Theorem

The 3.5 exterior angle theorem and triangle sum theorem are two fundamental theorems in geometry that provide insight into the relationships between angles and sides of triangles. The 3.5 exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the two opposite interior angles. Put another way, the sum of the three angles of a triangle is equal to the sum of two right angles, or 180 degrees. The triangle sum theorem states that the sum of all three angles of a triangle must be equal to 180 degrees.

## Understanding the 3.5 Exterior Angle Theorem The 3.5 exterior angle theorem is based on the concept that the sum of the three angles of a triangle is equal to 180 degrees. This theorem states that the measure of an exterior angle of a triangle is equal to the sum of the two opposite interior angles. This theorem is often represented as the equation A + B + C = 180°. In the equation, A, B and C represent the three angles of the triangle.

The 3.5 exterior angle theorem can be easily demonstrated with a triangle drawn on a piece of paper. It can be seen that when the three angles of the triangle are added together, they equal 180 degrees. Furthermore, when the exterior angle is added to the two opposite interior angles, it also equals 180 degrees. This demonstrates that the measure of the exterior angle is equal to the sum of the two opposite interior angles.

## Understanding the Triangle Sum Theorem The triangle sum theorem states that the sum of all three angles of a triangle must be equal to 180 degrees. This theorem is based on the fact that a triangle only has three sides, and therefore, the sum of its angles must be equal to 180 degrees in order to close the triangle. This theorem is often represented as the equation A + B + C = 180°, where A, B and C represent the three angles of the triangle.

The triangle sum theorem can be easily demonstrated with a triangle drawn on a piece of paper. It can be seen that when the three angles of the triangle are added together, they equal 180 degrees. This demonstrates that the sum of all three angles of a triangle must be equal to 180 degrees.

## Using the 3.5 Exterior Angle Theorem and Triangle Sum Theorem The 3.5 exterior angle theorem and triangle sum theorem are important theorems in geometry that can be used to calculate unknown angles and lengths in triangles. Knowing the values of two angles or two sides of a triangle, it is possible to use the 3.5 exterior angle theorem or triangle sum theorem to calculate the missing values. This can be useful in solving problems related to geometry, such as finding the length of a side of a triangle or the measure of an angle.

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The 3.5 exterior angle theorem and triangle sum theorem are two important theorems in geometry that provide insight into the relationships between angles and sides of triangles. The 3.5 exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the two opposite interior angles. The triangle sum theorem states that the sum of all three angles of a triangle must be equal to 180 degrees. Knowing these theorems can be useful in solving problems related to geometry.