Question

The four angles,in degrees,of quadrilateral ABCD are

Angle A=(x^2-105)

Angle B =(x^2-65)

Angle C =(470-30x)

AngleD=(510-30x)


Show that ABCD Is a trapezium .Show algebraic working

Answer 1

Trapezium is a quadrilateral, and we know that the internal angles of a quadrilateral are equal to 360° .

SO:---

Angle A+Angle B+Angle C+Angle D=360°
(x²-105)+(x²-65)+(470-30x)+(510-30x)=360°
2x²+810-60x=360°
2x²+810-60x-360°=0
2x²+450-60x=0
2x²-60x+450=0
2(x²-30x+225)=0
2(x-15)²=0
(x-15)²=0/2
x-15=√0/√2
x-15=0
x=15
After putting the values, you will get the following:-

Angle A=x²-105=15²-105=120°
Angle B=x²-65=15²-65=160°
Angle C=470-30x=470-30×15=20°
Angle D=510-30x=510-30×15=60°

So, As we know that, the sum of internal angles of a quadrilateral is 360°

So, 120°+160°+20°+60°=360°

Hence, proved/verified that it a trapezium (quadrilateral).