Question

In a pentagon

a) How many diagonals can be drawn from a vertex to other vertices?

b) How many triangles will be made by these diagonals?

c) What is the sum of angles of a pentagon ​

Answer 1

Answer:

two diagonals

For example, a pentagon (5 sides) has only 5 diagonals. Each vertex has two diagonals, so if you counted each diagonal from every vertex twice, you might think there were 10 diagonals.

Answer 2

Step-by-step explanation:

5 diagonal.

Each vertex has two diagonals, so if you counted each diagonal from every vertex twice, you might think there were 10 diagonals.

If we connect all vertices of a regular N-sided polygon we obtain a figure with = N (N - 1) / 2 lines. For N=8, the figure is: Careful counting shows that there are 632 triangles in this eight sided figure. All triangles are formed by the intersection of three diagonals at three different points.

So if we know that a pentagon adds up to 540 degrees, we can figure out how many degrees any sided polygon adds up to. Hexagon has 6, so we take 540+180=720. A heptagon has 7 sides, so we take the hexagon's sum of interior angles and add 180 to it getting us, 720+180=900 degrees.