Question

Prove that the sum of 4 angles of a quadrilaterals is ans

Answer 1

Answer:

answer is 360

Step-by-step explanation:

suppose in a quadrilateral sum of the angles are in ratio of 1:2:3:4

1a+2a+3a+4a=360

10a=360

a=360÷10

a=36

we got a =36 now,

1a=1×36=36

2a=2×36=72

3a=3×36=108

4a=4×36=144

now add them all,

36+72+108+144=360

hence proved .

Answer 2

To prove:

Sum of four angles of a quadrilateral is 360°.

Proof:

Construction:

Join A to C to form diagonal AC.

Now,

$\small{\angle CAD+\angle ADC+\angle ACD=180°----(i) }$

$\small{\angle ABC+\angle BAC+\angle ACB=180°---(ii)}$

(Angle sum property of Triangle)

(Angle sum property of Triangle)

Adding -------(i) and -------(ii),

$\small{{ \implies\angle ABC+\angle BAC+\angle ACB + \angle CAD+\angle ADC+\angle ACD} = 180 \degree + 180 \degree}$

$\small{{ \implies\angle ABC+\angle BAD +\angle ADC+\angle BCD} = 360 \degree}$

Hence Proved.