Question

In quadrilateral ABCD, side AB is parallel to side DC. If ∠A : ∠D = 1 : 2 and ∠C : ∠B = 4:5. 1) Calculate each angle of the quadrilateral. 2) Assign a special name to quadrilateral ABCD.

Answer 1

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

Step-by-step explanation:

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.