Question

In a quadrilateral ABCD, ∠A +∠C=140, ∠A:∠C=1:3 and ∠B:∠D=5:6, find angles A, B, C and D.

Answer 1

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Answer 2

The answers are, ∠A = 35°, ∠B = 100°, ∠C = 105°, and ∠D = 120°

GIVEN

In a quadrilateral ABCD, ∠A +∠C=140, ∠A:∠C=1:3 and ∠B:∠D=5:6.

TO FIND

Find angles A, B, C and D.

SOLUTION

We can simply solve the above problem as follows;

We know that sum of all angles of a quadrilateral is equal to 360°

Now,

∠A : ∠C = 1:3

Let, ∠A = x

∠C = 3x

ATQ

∠A + ∠C = 140°

x + 3x = 140

4x = 140

x = 140/4 = 35

∠A = 35°

∠C = 3 × 35 = 105°

Now,

∠A + ∠B + ∠C + ∠D = 360

∠B + ∠D = 360 - 140

∠B + ∠D = 220°

5x + 6x = 220

11x = 220

x = 220/11 = 20

∠B = 5 × 20 = 100°

∠D = 6 × 20 = 120°

Hence, The answers are, ∠A = 35°, ∠B = 100°, ∠C = 105°, and ∠D = 120°

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