Math, asked by yadavanshuman943, 11 months ago

show that sum of four angles of a quadrilateral is 360​

Answers

Answered by Zisha7
5

Answer:

We know that the sum of the angles of a triangle is 180°. ⇒ ∠A + ∠B + ∠C + ∠D = 360° [using (i) and (ii)]. Hence, the sum of all the four angles of a quadrilateral is 360°.

Answered by naavyya
3

Step-by-step explanation:

Consider a quadrilateral PQRS, QS is the diagonal.

To prove : ∠P + ∠Q + ∠R + ∠S = 360º

Proof:

In triangle PQS, we have,

∠P + ∠PQS + ∠PSQ = 180º ... (i)  [Using Angle sum property of Triangle]

Similarly, in triangle QRS, we have,

∠SQR + ∠R + ∠QSR = 180º ... (ii)  [Using Angle sum property of Triangle]

Adding (i) and (ii), we get ,

∠P + ∠PQS + ∠PSQ + ∠SQR + ∠R + ∠QSR = 180º + 180º

⇒ ∠P + ∠PQS + ∠SQR + ∠R + ∠QSR + ∠PSQ  = 360º

Also, ∠PQS + ∠SQR  = ∠PQR and ∠QSR + ∠PSQ = ∠PSR

⇒ ∠P + ∠Q + ∠R + ∠S  = 360º

Hence proved

Attachments:
Similar questions