Question

Prove that the sum of all angles of quadrilateral is 360⁰

Answer 1

Answer:

Hence Proved!!!

Step-by-step explanation:

Diagram:

• Refers to attachment.

Given:

• ABCD is a quadrilateral.

To Prove:

• ∠A + ∠B + ∠C + ∠D = 360º

Construction:

• Join BD.

Proof:

In ΔABD, we have

⇒ ∠A + ∠ABD + ∠ADB = 180º ...... (1)       [Angle sum property]

Similarly, In ΔBCD,

⇒ ∠DBC + ∠C + ∠BDC = 180º ...... (2)      [Angle sum property]

Now, add equation (1) and equation (2), we get

⇒ ∠A + ∠ABD + ∠ADB + ∠DBC + ∠C + ∠BDC = 180º + 180º

⇒ ∠A + ∠ABD + ∠DBC + ∠C + ∠ADB + ∠BDC  = 360º

⇒ ∠A + ∠B + ∠C + ∠D  = 360º

Hence Proved!!!

#answerwithquality

#BAL

Answer 2

$\huge\sf \orange{hello}....$

Statement :

sum of the angles of quadrilateral is 360°

To Prove :

∠A + ∠B + ∠C + ∠D = 360°

Proof :

In ∆ ABC , m∠4 + m∠5+m∠6 = 180°

[ using angle a property of a triangle]

Also , in ∆ ADC , m∠1 + m∠2+m∠3= 180°

Sum of the measures of ∠A, ∠B , ∠C and ∠D of a quadrilateral

m∠4 + m∠5+ m∠6 + m∠1 + m∠2 +m∠3 = 180°+ 180°

→ ∠A + ∠B + ∠C + ∠D = 360°

Thus , sum of measure of four angles of quadrilateral is 360°.