2
votes
1answer
21 views

finding parallel sides from a irregular decagon?

Is it possible to find out that which of two sides are parallel in this irregular decagon.If,it is yes;then how can I proceed? I have tried with "Consecutive Interior Angles".but can't come to a ...
1
vote
4answers
151 views

Proof that the number of diagonals of a polygon is $\frac{n(n-3)}{2} $

For $n \geq 3$ proof that the number of diagonals of a polygon is $\frac{n(n-3)}{2} $ using induction. I don't know how to start this problem, can you give me a hint?
2
votes
1answer
420 views

How many triangles are formed by $n$ chords of a circle? [duplicate]

This is a homework problem I have to solve, and I think I might be misunderstanding it. I'm translating it from Polish word for word. $n$ points are placed on a circle, and all the chords whose ...
1
vote
4answers
482 views

How can I prove that exterior angles of a pentagon add up to four right angles?

How can I prove that exterior angles of a pentagon add up to four right angles I have thought about dividing the pentagon into 3 triangles, then maybe using the exterior angle sum equal to two ...