Question

Find the measure of x in the given figure.​

Answer 1

Hello, Buddy!!

||Required Solution||

Given,

All the sides of a Pentagon are equal[Regular Pentagon].

One of the angle is x

WKT

• Angles opposite to equal sides are equal.
• Sum of all interior angles is 540°

Hence,

→ x+x+x+x+x = 540°

→ 5x = 540°

→ x = 540°/5

→ x = 108°

• Value of x ➪ 108°

@MrMonarque♡

Hope It Helps You ✌️

Answer 2

Answer:

108°

Step-by-step explanation:

Let the pentagon be ABCDE.

Since ABCDE is equilateral, therefore we can also say that the angles lying in its interior are equal making the pentagon equiangular as well.

Now, using ( n − 2 ) × 180° where n=number of sides of the polygon,

(5-2) x 180° = 3 x 180° = 540°

Since the pentagon is equiangular, therefore, ∠A=∠B=∠C=∠D=∠E=x -- 1

Therefore, putting values of equation 1 in angle sum of interior angles of pentagon:

∠A+∠B+∠C+∠D+∠E=540°

-> x+x+x+x+x = 540°

5x=540°

x=540°/5

x=108°