Question

In a quadrilateral ABCD, side AB is parralel to CD, if angle A: angle B = 1 : 2 and angle C : angle D = 4 : 5, calculate each angle of the quadrilateral​

Answer 1

Answer:

Let A and D be 1x and 2x respectively.

A+D=180°. [AB¶CD] {interior angles on same side of transversal}

x+2x=180°

3x=180°

x=60°

Therefore A=60°, D=120°

also,

let C and B be 4y and 5y respectively.

C+B=180°. [AB¶CD] {interior angles on same side of transversal}

4y+5y=180°

9x=180°

y=20°

Therefore C=80°, B=120°

Trapezium can be the quadrilateral ABCD, where two sides are parallel.

Answer 2

A:B = 1:2

C:D = 4:5

Let the ratios be x

Sum of angles in a quadrilateral = 360°

1x + 2x + 4x + 5x = 360°

12x = 360°

x = 30°

angle A = 30°

angle B = 60°

angle C = 120°

angle D = 150°