Question

Find the angle measure x in the following figures

A. $ 108^\circ $
B. $ 105^\circ $
C. $ 72^\circ $
D. $ 110^\circ $

Answer 1

Hint: Here, we are given the closed figure with five equal sides and so this figure is known as pentagon. We know that the sum total of all the interior angles is equal to $ 540^\circ $ . With the help of the property that - the angle of the equal side is equal.

Complete step-by-step answer:
Here we are given that the pentagon is having all its side equal.
It implies that all the interior angles are also equal.
Let the interior angle of the pentagon is $ = x $
By using the property that – sum of all the five interior angles is equal to $ 540^\circ $
 $ \Rightarrow 5x = 540 $
When any number multiplicative with the term changes its side then it goes to the division of the opposite side and vice-versa.
 $ \Rightarrow x = \dfrac{{540}}{5} $
Simplify the above equation –
 $ \Rightarrow x = 108^\circ $
Therefore, the required answer – the angle measure x in the given pentagon figure is $ 108^\circ $
Hence, from the given multiple choices – the option A is the correct answer.
So, the correct answer is “Option A”.

Note: Always remember the basic formula for the sum of the interior angles of a polygon with “n” sides is equal to the $ = (n - 2) \times 180^\circ $ place the value of the “n” where “n” is the number of sides of any closed figure. Common words, they are said to be polygons. Polygons with five sides are called pentagon and polygons with ten sides are called decagon. Here we were given equal sides so it went for equal measure of angles, at times you may be given relation or the ration of the five angles.