Question

in a quadrilateral ABCD,angleA,anglB,anglC,anglD are in the ratio 2:4:6:8.find the angle
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Answer 1

Let

• ∠A = 2x
• ∠B = 4x
• ∠C = 6x
• ∠D = 8x

Concept used:

⟶ Sum of all Angles in a Quadrilateral is always 360°.

This is known as 'Angle Sum Property'

Applying the above concept,

2x + 4x + 6x + 8x = 360°

⇒ 20x = 360°

⇒ x = 360 ÷ 20

⇒ x = 18°

Now let's find the measure of each angle of the Quadrilateral

∠A = 2x = 2(18) = 36°

∠B = 4x = 4(18) = 72°

∠C = 6x = 6(18) = 108°

∠D = 8x = 8(18) = 144°

∴ The angles are 36°, 72°, 108° and 144°

Verification:

You can verify whether the above angles are correct are not by adding them.

If they sum up to 360°, → the measures are correct

Here,

36° + 72° + 108° + 144° = 360°

360° = 360°

LHS = RHS

★ Hence Verified ★

Learn the derivation of Angle Sum Property:

We know that diagonal of a Quadrilateral divides it into 2 Triangles.

Sum of all angles in a triangle is 180°

Since there are 2 Triangles,

2 × 180° = 360°