What is the sum of the interior angles of the polygon shown below?

Mathematics

2 answers:

Alinara [238K]3 years ago

7 0

Answer:

Sum of interior angle = 900

Step-by-step explanation:

It has 7 sides

Sum of angle for a polygon = (n-2)180

7 sides= (7-2)180

Sum of angle = 5*180

" = 900

crimeas [40]3 years ago

3 0

Answer: 360 degrees!

Step-by-step explanation: To find the sum of the interior angles, multiply the number of triangles by 180. C) The sum of the interior angles in any polygon can be found by multiplying the number of triangles formed by the diagonals from one vertex times 180 degrees in each triangle. Hope this helps, have a wonderful day! :D

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Tim must read 2 books from a list of 7 recommended books for his summer reading program. In how many different ways can Tim choo

Marianna [84]

There are 21 ways Tim choose 2 books from the 7 recommended book

Solution:

Given that Tim must read 2 books from a list of 7 recommended books for his summer reading program

To find: different ways can Tim choose 2 books from the 7 recommended books

This is a combination problem

A combination is a selection of all or part of a set of objects, without regard to the order in which objects are selected

The formula for combinations is:

$n C_{r}=\frac{n !}{r !(n-r) !}$

where n represents the number of items, and r represents the number of items being chosen at a time

Here we have to choose 2 books from 7 books

Therefore, n = 7 and r = 2

Substituting values in above formula, we get

$\begin{aligned}&7 C_{2}=\frac{7 !}{2 !(7-2) !}\\\\&7 C_{2}=\frac{7 !}{2 ! \times 5 !}\end{aligned}$

For a number n, the factorial of n can be written as,

$n !=n \times(n-1) \times(n-2) \dots \dots \times 2 \times 1$

Therefore, we get

$7 C_{2}=\frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1 \times 5 \times 4 \times 3 \times 2 \times 1}\\\\7C_2 = 7 \times 3 = 21$