Question

prove that the sum of the angles of a quadrilateral is 4 right angles​

Answer 1

$\bf \underline \blue{Question : - }$

prove that the sum of the angles of a quadrilateral is 4 right angles ?

$\bf \underline \blue{Answer : - }$

Concept:-

• The sum of all angles of a triangle is 180°

• Consider a quadrilateral as ABCD.

Construct:-

BD as a diagonal!!!

To Prove:-

∠A + ∠B + ∠C + ∠D =4 Right Angles

Solution:-

now,

Apply angle sum property in ∆ ABD.

∠A + ∠ABD + ∠BDA = 180° ..............(1)

Apply angle sum property in ∆ BCD.

∠C + ∠DBC + ∠ BDC = 180° ..............(2)

Adding equation (1) and (2)...

∠A + ∠ABD + ∠BDA + ∠C + ∠DBC + ∠ BDC= 180°+180°=360°

(or)

∠A + ∠ABD + ∠BDA + ∠C + ∠DBC + ∠ BDC=4 × 90° = 4 right angles...

Hence Proved!!!