Question

Prove that the sum of all angles of a quadrilateral is 360○

Answer 1

let 4 angles be ABCD
A=X
B=2X
C=3X
D=4X
Sum of all angles of quadrilateral =360
A+B,+C+D=360
X+2X+3X+4X=360
10X=360
x=360/10
x=36
now all the angles,
A=36
B=2×36=72
C=3×36=108
D=4×36=144
this all angles sum is 360

Answer 2

Data: ABCD is a quadrilateral
TPT: Angle A+angle B +angle C+angle D=360°
Construction : Join D and B
Proof : In Triangle ABD
Angle ABD +Angle BDA +Angle DAB = 180° - equation 1 (angle sum property of a triangle)
In Triangle DCB
Angle DCB +Angle CBD+ Angle BDC=180°-equation 2 (angle sum property of a triangle)
Angle ABD +Angle BDA +Angle DAB +Angle DCB +Angle CBD +Angle BDC =180+180
(Angle ABD +Angle CBD) +(Angle ADB+Angle BDC) +Angle DAB +DCB =360°
Angle B +Angle D +Angle A +Angle C=360 °
Angle A +Angle B +Angle C +Angle D =360 °