Question

In the adjoining figure ABCD is a trapezium. If angle A : angle D=5:7, B= (3x+11)° and angle C= 5x-31)°, then find all the angles of the trapezium​

Answer 1

Answer: 19

Step-by-step explanation:

Let the altitude of angle A and D be 5x and 7x respectively.

We know that the sum of the angles of a trapezium is 360°.

So, according to the given question

∠A + ∠B+ ∠C + ∠D = 360°

$5x + 7x + (3x + 11) + (5x - 31) = 360°$

$5x + 7x + 3x + 5x + 11 - 31 = 360$

$20x -20 = 360$

$x = \frac{360 + 20}{20}$

$x = \frac{380}{20}$

$x = 19$

Answer 2

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Let the altitude of angle A and D be 5x and 7x respectively.

We know that the sum of the angles of a trapezium is 360°.

So, according to the given question

∠A + ∠B+ ∠C + ∠D = 360°

$5x + 7x + (3x + 11) + (5x - 31) = {360}^{o} \\ 5x + 7x + 3x + 11 - 31 = {360}^{o} \\ 20x - 20 = {360}^{o} \\ x = \frac{360 + 20}{20} \\ x = \frac{380}{20} \\ x = 19$