In a quadrilateral ABCD, angle B + angle D = 140 degrees, angle B is to angle D is -- 1:3
and angle A : angle C = 5:6. Find all the angles of the quadrilateral

Question

In a quadrilateral ABCD, angle B + angle D = 140 degrees, angle B
is to angle D is -- 1:3
and angle A : angle C = 5:6 Find all the angles of the
quadrilateral

Manbar Singh · Accepted Answer

Dear Student,

Please find below the solution to the asked query :

We have ABCD as the given quadrilateral
Let ∠B = x and ∠D = 3xNow, ∠B + ∠D = 140°⇒x + 3x = 140°⇒4x = 140°⇒x = 35Now, ∠B = x = 35°; ∠D = 3x = 3×35 = 105°Let ∠A = 5y ; ∠C = 6ynow, ∠A + ∠B + ∠C + ∠D = 360°  angle sum property⇒5y + 35° + 6y + 105° = 360°⇒11y = 220⇒y = 20So, ∠A = 5×20 = 100°∠C = 6×20 = 120°

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In a quadrilateral ABCD, angle B + angle D = 140 degrees, angle B is to angle D is -- 1:3 and angle A : angle C = 5:6. Find all the angles of the quadrilateral

In a quadrilateral ABCD, angle B + angle D = 140 degrees, angle B is to angle D is -- 1:3
and angle A : angle C = 5:6. Find all the angles of the quadrilateral