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ABCD is a trapezium such that AB||CD, ∠A : ∠D = 2 :1, ∠B : ∠C = 7 : 5. Find the angles of the trapezium.

Solution:

Given, ABCD is a trapezium such that AB || CD.

∠A : ∠D = 2 :1 and ∠B : ∠C = 7 : 5.

We have to find the angles of the trapezium.

Let the angles A and D be 2x and x.

We know that the angles on either side of the base of a trapezium are supplementary.

So, 2x + x = 180°

3x = 180°

x = 180°/3

x = 60°

So, A = 2x = 2(60°) = 120°

Let the angles B and C be 7x and 5x.

7x + 5x = 180°

12x = 180°

x = 180°/12

x = 18°

So, B = 7x = 7(18°) = 105°

C = 5x = 5(18°) = 75°

Therefore, the angles of the trapezium are 120°, 105°, 75° and 60°.

✦ Try This: Adjacent sides of a rectangle are in the ratio 5 : 12, if its perimeter is 34 cm. Find the length of the diagonal.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 174

Summary:

ABCD is a trapezium such that AB||CD, ∠A : ∠D = 2 :1, ∠B : ∠C = 7 : 5. The angles of the trapezium are 120°, 105°, 75° and 60°.

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