Question

The four angles, in degrees, of quadrilateral ABCD are

angle A = (x² – 105)
angle B = (x² – 65)
angle C = (470 – 30x)
angle D=(510-30x)
Show that ABCD is a trapezium.
Show clear algebraic working.

Answer 1

Explanation:

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).

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