In how many ways can a pair of parallel diagonals of a regular polygon of 10 sides be
selected?
Answers
Answer:
53
Step-by-step explanation:
The answer is 53
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Answer:
45 Ways
Step-by-step explanation:
In how many ways can a pair of parallel diagonals of a regular polygon of 10 sides be selected
if we label Vertices A₁ , A₂ , ........... A₁₀
the Let see Parallel diagonals from Vertices A₁
A₂A₁₀ ,A₃A₉. A₄A₈ , A₅A₇ are parallel to each other
total 4 and 2 to be selected
⁴C₂ = 6
A₂A₉ , A₃A₈ , A₄A₇ are parallel (A₁A₁₀ & A₅A₆ are sides not diagonals)
³C₂ = 3 Ways
=> 6 + 3 = 9 Ways
Like A₁ total are 10 vertices
=> 10 * 9 = 90 Ways
but from A₆ , Parallel diagonals are same like from A₁
so opposite vertices will have same pair to choose
a pair of parallel diagonals can be selected in = 90/2 = 45 Ways