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

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∠ A = 120 °, ∠ B = 105 °, ∠ C = 75 °, ∠ D = 60 °

∠ A = 100 °, ∠ B = 105 °, ∠ C = 70 °, ∠ D = 60 °

∠ A = 150 °, ∠ B = 105 °, ∠ C = 75 °, ∠ D = 60 °

∠ A = 120 °, ∠ B = 125 °, ∠ C = 85 °, ∠ D = 50 °

answer is A.

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Detailed Solution

Given that, ABCD be a trapezium, where

A B ∥ C D

.
Assuming the measure of angle A and D be 2x and x, respectively.
Since in trapezium the angles on either side of the base are supplementary.

\Rightarrow 2 x + x = 180^{\circ}

\Rightarrow 3 x = 180^{\circ}

\Rightarrow x = \frac{180^{\circ}}{3}

\Rightarrow x = 60^{\circ}

∠ A = 2 × 60 ° = 120 °

and

∠ D = 60 °

.
Now, assuming the measure of angle B and C be 7x and 5x respectively.
Since in trapezium the angles on either side of the base are supplementary.

\Rightarrow 7 x + 5 x = 180^{\circ}

\Rightarrow 12 x = 180^{\circ}

\Rightarrow x = \frac{180^{\circ}}{12}

\Rightarrow x = 15^{\circ}

So,

∠ B = 7 × 15 = 105 °

and

∠ C = 5 × 15 = 75 °

.
Thus,

∠ A = 120 ° ∠ B = 105 °, ∠ C = 75 °

and

∠ D = 60 °

.
Hence, option 1 is correct.

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