MathsLines and AnglesTrianglesLogic behind the Sum of all Angles of a Triangle

Logic behind the Sum of all Angles of a Triangle

Table of Contents

  • Sum of Angles of a Triangle
  • What’s Next?

In the previous segment, we learnt about Perpendicular transversals. In this segment, we will learn a bit more about the angles within a triangle.

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    How is the sum of angles of a triangle always 180°?

    The sum of the angles of a triangle always equals 180°.

    Let us understand the logic behind this with the help of the following example:

    Consider triangle ABC.

    Logic behind the Sum of all Angles of a Triangle is 180

    Cut the triangle into 3 parts as shown below:

    Logic behind the Sum of all Angles of a Triangle is 180

    Now, there are three parts: AEDF, EBD, and FCD.

    Logic behind the Sum of all Angles of a Triangle is 180

    Rotate each of these parts in such a way that A, B, and C meet at a single point. The resultant figure will look like this:

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