Question

Find the value of W

​

Answer 1

`{\huge{\fcolorbox{purple}{blue}{\red{\boxed{\boxed{\boxed{\boxed{\underbrace{\overbrace{\mathfrak{\pink{\fcolorbox{green}{yellow}{Answer}}}}}}}}}}}}}`

To find :-

The value of x in the angles of Pentagon

Given :-

Here we have been provided 5 angles in Pentagon

x°, (x - 44)°, (x + 6)°, 125°, and 117°

Solution :-

We will find the value of x with the angle sum property.

Now, we will find the sum of angles of Pentagon

there is a formula

(n - 2) × 180°

n = no. of sides of above shape

here n = 5

(5 - 2) × 180°

3 × 180° = 540°

Now will add the above given angle in the diagram and put equal to 540°.

x° + (x - 44)° + (x + 6)° + 125° + 117° = 540° (angle sum property)

`3x + 204{\degree} = 540{\degree} \\ 3x = 540{\degree} -204{\degree} \\ 3x = 336{\degree} \\ x = \frac{336{\degree}}{3} \\ x = 112{\degree}`

x = 112°

further we will find further 2 angles related to x.

x - 44 = 112 - 44 = 68°

x + 6 = 112 + 6 = 118°

Result :-

The all angles of Pentagon are

125°, 117°, 118°, 112°, and 68°.

Answer 2

`\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}`

`sum \: of \: angles\: of \: a \: polygon \: = \\(n - 2) * 180\degree`

in the question , we've been given a five sided figure , i.e. , a pentagon.

sum of angles of a pentagon = ( 5 - 2 ) × 180°

`\implies \: 3 * 180\degree \\ \implies \: 540\degree`

thus we can say that ,

angle sum property of pentagon states that the sum of all the angles of a pentagon equals 540°.

therefore ,

Explanation:

`125\degree + 117\degree + (x + 6)\degree + x + (x - 44)\degree = 540\degree \\ \\ 125\degree + 117\degree + x + 6\degree + x + x - 44\degree = 540\degree \\ \\ 204\degree + 3x = 540\degree \\ \\ 3x = 540\degree - 204\degree \\ \\ 3x = 336\degree \\ \\ x = \cancel(336)/(3) \\ \\ x = 112\degree`

hope helpful ~