Question

Q3.The sum of the four angles of the quadrilateral is……………….. *​

Answer 1

Answer:

The sum of the four angles of the quadrilateral is 360 degrees.

Step-by-step explanation:

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Answer 2

The sum of the four angles of the quadrilateral is 360°.

Explanation:

Quadrilateral :

• A quadrilateral is a polygon that has four sides.
• As we know, a quadrilateral has four sides, 4 vertices, 4 angles, and 2 diagonals.

ANGLE-SUM PROPERTY OF A QUADRILATERAL :

The sum of the four angles of a quadrilateral is always four right angles or 360°.

Verification :  

• Draw a quadrilateral ABCD and draw a diagonal; let BD.
• Now, 2 triangles ∆DBC and ∆ABD are formed.
• Mark the angles of two triangles as 1, 2, 3, and 4, 5, 6, as shown in the figure below.

Now, by using the angle-sum property of a triangle in ∆DBC and ∆ABD :

∠1 + ∠2 + ∠3 = 180° for ∆DBC ... (1)

and ∠4 + ∠5 + ∠6 = 180° for ∆ADB ….. (2)

Adding eq.(1) and (2), we get

(∠1 + ∠4) + ∠2 + (∠3 + ∠5) + ∠6 = 180° + 180° = 360°

∠D + ∠C + ∠B + ∠A = 360°, ie.

∠A + ∠B + ∠C + ∠D = 360°

Hence, the sum of four angles of a quadrilateral is 360°.

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