Question

Find the angle measure x.​

Answer 1

Answer:

108°

Step by step explanation:

Construction:

Let us join vertices AD and AC as shown to form three triangles as shown. We have used numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 to represent interior angles of triangle for our convenience.

Solution :

Since the sum of interior angles of a triangle is 180°

In △ABC,

∠(6+5+4) = 180° (Angle sum property of a triangle)

In △ACD,

∠(7+2+3) = 180° (Angle sum property of a triangle)

In △EAD,

∠(1+9+8) = 180° (Angle sum property of a triangle)

Therefore, Sum of interior angles of the pentagon is

=∠(1+2+3+4+5+6+7+8+9)

=180°+180°+180° [using the above three results]

=540°

i.e. ∠A+∠B+∠C+∠D+∠E=540°

From the above proof we can conclude that it is a regular Pentagon and therefore, 

∠A=∠B=∠C=∠D=∠E

or Each angle = (540/5)°

⇒ Value of each angle = 108°

Hence, each angle of a regular pentagon or value of x = 108°