Adding the Angles in a Triangle

Student Summary

A 180∘180^\circ angle is called a straight angle because when it is made with two rays, they point in opposite directions and form a straight line.

A line with point marked. Angle is marked 180 degrees. 

If we experiment with angles in a triangle, we find that the sum of the measures of the three angles in each triangle is 180∘180^\circ— the same as a straight angle!

Through experimentation we find:

  • If we add the three angles of a triangle physically by cutting them off and lining up the vertices and sides, then the three angles form a straight angle.

  • If we have a line and two rays that form three angles added to make a straight angle, then there is a triangle with these three angles.

    A triangle. The angles are colored blue, red, and green. A line with two rays forming three angles. The angles are colored blue, red, and green.

Visual / Anchor Chart

Standards

Building On
7.G.2

7.G.A.2

Addressing
8.G.2

8.G.5

8.G.A.2

8.G.A.5

8.G.5

8.G.A.5