Question

Explain how to use what you know about the sum of the angles in a triangle to figure out the sum of the angles of quadrilateral abed

Answer 1

Answer:

See attached image and explanation below.

Step-by-step explanation:

We notice that any quadrilateral abed can be divided into two triangles by drawing one of the quadrilateral's diagonals. See the attached picture where the quadrilateral is noted with a green perimeter,  the diagonal is pictured in red, and the triangles that are form are shaded in light blue and beige.

Each of the triangles in which the quadrilateral is divided, has the property that the addition of its internal angles equals 180 degrees. From the picture we understand that in order to find what the addition of the internal angles of the quadrilateral is, all we need to do is to add all the angles in both triangles.

Such addition will render 360 degrees. And since the diagonal division can be done with a quadrilateral of any shape, we conclude that the addition of the internal angles of any quadrilateral should result in 360 degrees.