# In a quadrilateral ABCD angle B + angle D =140 degree angle B : angle D = 1:3 and angle A : angle C = 5:6 find all the angles of the quadrilateral.

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by ishu2920

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by ishu2920

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1x+3x=140 degree

4x=140 degree

x=140/4=35

ang B=35 dgree

ang D=105 degree

360-140=220 degree

ang A + ang C=220 degree

5x+6x=220 degree

11x=220 degree

x=220/11

=20

ang A=100

ang B=120

Let angle B = x and angle D = 3x

Ratio of angle A and angle C = 5 : 6

Let angle A = 5x and angle C = 6x

But Angle B + angle D = 140°

x + 3x = 140°

4x = 140°

x = 35°

Angle B = x = 1 × 35 = 35°

Angle D = 3x = 3 × 35 = 105°

As the sum of B and D is 140 degrees....therefore, the sum of angles A and C is equal to 220 degrees

5x + 6x = 220 ⇒ x = 20°

angle A = 5×20 = 100 °

angle C = 6 × 20 = 120°