Question

The sum of four angles of quadrilateral is equal to __________

(a) 90°

(b) 360°

(c) 180°

(d) 270°

This question was posed to me in exam.

I want to ask this question from Quadrilaterals Basics in division Quadrilaterals of Mathematics – Class 9

Answer 1

Correct option is (b) 360°

For explanation I would say: Let’s take a quadrilateral as shown in figure. By dividing it diagonally, we can see that it breaks into two triangles.

We know that sum of three angles of any triangle is equal to 180°.

Hence, ∠QPR + ∠Q + ∠QRP = 180° and ∠SPR + ∠S + ∠PRS = 180°.

Now to get the sum of four angles of quadrilateral,

∠P + ∠Q + ∠R + ∠S = (∠QPR + ∠SPR) + ∠Q + (∠QRP + ∠PRS) + ∠S

= (∠QPR + ∠Q + ∠QRP) + (∠SPR + ∠S + ∠PRS)

= 180° + 180°

= 360°