Question

Prove x = α +β+ γ ( using figure given )

Answer 1

In the given figure, We have at a point ∠x

Because at a given point, angle measures to be 360°.

∴ Other angle = 360° - x

Now, In the enclosed figure ( which is also a quadrilateral because It has four sides. )

We know,

⇒ Sum of all interior angles of a Quadrilateral = 360°

⇒ ɑ + β + Ɣ + (360° - x) = 360°

⇒ ɑ + β + Ɣ - x = 360° - 360°

⇒ ɑ + β + Ɣ - x = 0

⇒ ɑ + β + Ɣ = x

Hence, Proved.

Some Information :-

☛ The sum of all interior angles of a triangle is 180° while the sum of all interior angles of a quadrilateral is 360°.

☛ A quadrilateral is closed figure enclosed by four sides.

Square, Rectangle, Rhombus, are some examples of a quadrilateral.

☛ A point in a given plane measures 360°.

Answer 2

Because at a given point, angle measures to be 360°. Now, In the enclosed figure ( which is also a quadrilateral because It has four sides. ) Hence, Proved. ☛ The sum of all interior angles of a triangle is 180° while the sum of all interior angles of a quadrilateral is 360°.