# in how many ways can a pair of parallel diagonals of a regular polygon of 10 sides be selected

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## The number of pairs of diagonals of a regular polygon of `10` sides that are parallel are

The number of pairs of diagonals of a regular polygon of `10` sides that are parallel are A. `45` B. `56` C. `22` D. `64`

The number of pairs of diagonals of a regular polygon of10 10

sides that are parallel are

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## The number of pairs of diagonals of a regular polygon of 10 sides that are parallel are

(a) Fix a vertex A. There are 4 parallel diagonals. There are 5 such sets since the vertices of the 10-gon can be paired into 5 sets. In each set there are "^(4)C(2) pairs, i.e, a total of "^(4)C(2)xx5=30 pairs of diagonals. Now fix a side AB. There are 3 parallel diagonals and 5 such sets. So, total pairs =^(3)C(2)xx5=15 Hence, net total =30+15=45

The number of pairs of diagonals of a regular polygon of

10

sides that are parallel are

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Text Solution A 45 B 56 C 22 D 64 Answer

The correct Answer is A

Solution ( a )

Fix a vertex A . There are 4 parallel diagonals. There are 5

such sets since the vertices of the

10

-gon can be paired into

5

sets. In each set there are

4 C 2

pairs, i.e, a total of

4 C 2 × 5 = 30 pairs of diagonals. Now fix a side A B . There are 3

parallel diagonals and

5 such sets. So, total pairs = 3 C 2 × 5 = 15 Hence, net total = 30 + 15 = 45 Answer

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यदि एक नियमित बहुभुज में भुजाओं की संख्या 10 है तो विकर्णों की संख्या होगी?

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645006448 Text Solution

The number of pairs of diagonals of a regular polygon of

10

sides that are parallel are

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## In how many ways can a pair of parallel diagonals of a regular polygon of 10 sides be selected?

Answer (1 of 2): There are diagonals that are parallel to a side, and diagonals that aren’t parallel to a side of the polygon. First we look at diagonals parallel to a side of the polygon There are 5 pairs of opposite sides, and each of these pairs is parallel. For each of these pairs you have...

In how many ways can a pair of parallel diagonals of a regular polygon of 10 sides be selected?

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Sort Jacob Sarkar

Studying('21-'23expected) from Ramakrishna Mission Vidyapith, DeogharAuthor has 155 answers and 146.8K answer views2y

Here, for 10 sided polygon….

So, let's know the formula first….

This proof was shown by Sir Doug Dillon as answer to the question How do I find the number of parallel diagonals in a polygon?

Now, let's come to this problem

So answer is 45 pairs…

Note- A decagon has n(n+3) n(n+3) = 35 35 diagonals diagonals

But, one diagonal may form the parallel pair with more than one diagonal!!!

✍️ Jacob Sarkar.

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There are diagonals that are parallel to a side, and diagonals that aren’t parallel to a side of the polygon.

First we look at diagonals parallel to a side of the polygon

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Bisect means to cut into two equal sides.

3 points have 3 joining lines including 3 sides of the triangle so has 0 diagonals

4 points have 6 joining lines including 4 sides of the square so has 2 diagonals

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A diagonal requires two vertices.

=> C(12,2) = 12!/2! 10! = 66 lines can be drawn using any 2 points.

But 12 lines form the sides of the polygon.

=> 66 - 12 = 54 Diagonals can be drawn.

:-)

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We will just draw the diagonals one after the other. When we begin before any are drawn, there is one region. Each diagonal adds at least one region, plus one more for every previously drawn diagonal it crosses. Thus the total number of regions is:

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