Question

find the value of x plz use a pic to explain me i will make u brainlist , in the back side of my book it's answer is 108 but I need explanation plz help me.​ plz answer fast

Answer 1

Step-by-step explanation:

Solution :-

From the given figure

In PQRST , PQ = QR = RS = ST = TP

=> All sides are equal

=> All angles are equal

=> It is a regular polygon of 5 sides

=> It is a regular Pentagon

The number of sides in the given figure = 5

n = 5

Given that

Interior angle = x°

We know that

Each interior angle of a regular polygon of n sides is [(n-2)/n]×180°

=> x° = [(5-2)/5]×180°

=> x° = (3/5)×180°

=> x° = (3×180°)/5

=> x° = 540°/5

=> x° = 108°

Therefore, The value of x = 108°

Answer:-

The measure of the angle x = 108°

Used formulae:-

→ Each interior angle of a regular polygon of n sides is [(n-2)/n]×180°

Answer 2

Answer:

Since the pentagon is a regular pentagon, we know that all sides of the polygon will be equal. Hence, all the interior angles of the pentagon will also be equal.

But why 108 degrees? That is the question.

Let us consider the exterior angles of the pentagon for a second. We know that since all the interior angles are equal, all the exterior angles will be equal as well. In fact, all the exterior angles will be equal to (180-x) degrees.

[We can derive this by using the linear pair property. As we can see, angles 1 and x will be linear pairs. Hence, angle 1 + angle x = 180 => angle 1 = (180 - angle x).]

Now, here comes another important property: The sum of all the exterior angles of ANY polygon is always equal to 360 degrees.

Also, we have already derived that there will be 5 exterior angles, each of measure (180-x). So, total sum of exterior angles = 5*(180-x) = 900-5x

This must be equal to 360.

Hence, 900-5x=360

=> 540 = 5x

=> x = 108

Hence, the measure of each interior angle of the polygon will be 108 degrees.

NOTE: The method that I have used above can also be used to derive a general formula: Sum of all of the interior angles of ANY polygon = (n-2) * 180, where n = number of sides. If you use this formula (which I would suggest as it is not easy to calculate the interior angle of large polygons like decagons. For calculating the measure of each interior angle, all you have to do is calculate the total sum of interior angles and divide it by the number of sides. This works only if the polygon is regular, i.e., all sides are equal.), you will get the same answer.

Hope this helps you.... please mark this answer as the brainliest.