Question

ABCD is a trapezium, such that ABǁCD. A:D=7:2 and B: C=4:5 .Find the angles of the trapezium ?​

Answer 1

Answer ::

The measure of all angles of trapezium are :-

• ∠A = 140°
• ∠B = 80°
• ∠C = 100°
• ∠D = 40°

Step-by-step explanation ::

To Find :-

• The angles of the trapezium

Given that,

• AB || CD
• A : D = 7 : 2
• B : C = 4 : 5

Solution :-

Let us assume the measure of the angles of trapezium,

• A : D = 7 : 2 as 7x : 2x
• B : C = 4 : 5 as 4y : 5y,

By a property of trapezium, as we know that,

The adjacent angles of trapezium are supplementary [ 180° ],

• ∠A + ∠D = 180° . . . equation 1
• ∠B + ∠C = 180° . . . equation 2

From equation 1 ::

➠ ∠A + ∠D = 180

➠ 7x + 2x = 180

➠ 9x = 180

➠ x = 180/9

➠ x = 20

The angles are :-

• 7x = 7*20 = 140°
• 2x = 2*20 = 40°

From equation 2 ::

➠ ∠B + ∠C = 180

➠ 4x + 5x = 180

➠ 9x = 180

➠ x = 180/9

➠ x = 20

The angles are :-

• 4x = 4*20 = 80°
• 5x = 5*20 = 100

The measure of all angles of trapezium are :-

• ∠A = 140°
• ∠B = 80°
• ∠C = 100°
• ∠D = 40°