Thus, by the Exterior Angle Theorem, the sum of those angles is equal to the measure of the exterior angle. We have. While not always necessary, we can check our solution using our previous knowledge of lines.
https://www.wyzant.com/resources/lessons/math/geometry/triangles/angles_of_triangles
The two angles that are not adjacent, or next to, the exterior angle of the triangle are called remote interior angles. Now that we know what these terms mean, we are ready for a theorem that will help us tremendously in our proofs.
https://www.wyzant.com/resources/lessons/math/geometry/triangles/angles_of_triangles
The Sum of the Angles in a Triangle. Introduction: The sum of the angles in a triangle is 180º. We show why that is true and give several examples. The Lesson: In the diagram shown above, we see triangle ABC and the dotted line through A that is parallel to BC. Since angle A, from the triangle, and angles 1 and 2 form a straight (dotted) line, the sum of their measures is 180º.
http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_TrianglesSumAngles.xml
1 Relationship between measurement of the sides and angles in a Triangle: The largest interior angle and side are opposite each other. 2  The same rule applies to the smallest sized angle and side and the middle sized angle and side.
http://www.mathwarehouse.com/geometry/triangles/
Interior Angles of a Triangle Rule. This may be one the most well known mathematical rule-The sum of all 3 interior angles in a triangle is 180°. As you can see from the picture below, if you add up all of the angles in a triangle the sum must equal 180°. This property of a triangle's interior angles is simply a specific example of the general rule for any polygon's interior angles.
http://www.mathwarehouse.com/geometry/triangles/
1 Interior angles (angles on the inside) sum up to 180°. 2  Triangle Inequality Theorem: This theorem states that the sum of the lengths of any 2 sides of a triangle must be greater than the third side.
http://www.mathwarehouse.com/geometry/triangles/
We also know that since the dotted line is parallel to BC that by alternate interior angles. This gives us: Substituting for angles 1 and 2 we have This result is true for all triangles: Summarizing:Theorem: The sum of the three angles in a triangle is always 180º. Let's Practice:If two of the three angles in a triangle have measure 34º and 72º, what is the measure of the third angle? We have 34º + 72º = 106º. Therefore the third angle has a measure of 180º - 106º = 74º In a triangle ABC, we have.
http://www.algebralab.org/lessons/lesson.aspx?file=Geometry_TrianglesSumAngles.xml
No matter how you position the three sides of the triangle, the total degrees of all interior angles (the three angles inside the triangle) is always 180°.
http://www.mathwarehouse.com/geometry/triangles/
Triangle Angle Sum Theorem. The sum of the measures of the interior angles of a triangle is 180. The diagram above illustrates the Triangle Angle Sum Theorem. Let's do some examples involving the Triangle Sum Theorem to help us see its utility.
https://www.wyzant.com/resources/lessons/math/geometry/triangles/angles_of_triangles
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. Adding the measures of the two remote interior angles of a triangle gives the measure of the exterior angle.
https://www.wyzant.com/resources/lessons/math/geometry/triangles/angles_of_triangles
what is the sum of three angles in the triangle
The sum of three angles in the triangle is 180º.