Question

in a quadrilater abcd ,the a,b,c and d are in the ratio 1:2:4:5.find the measure of each angle of the quadrilateral. write only answer

Answer 1

Given:

✭ ABCD is a quadrilateral

✭ Angles are on the ratio 1:2:4:5

To Find:

◈ The measure of each Angle?

Solution:

Concept

So here we may assume the angles with x and then we shall equate their sum to 360° to find our Answer!!

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So here let the Angles be,

• 1x
• 2x
• 4x
• 5x

So we know that their sum will be equal to 360°. Because in a quadrilateral angles add up to 360°

➝ 1x+2x+4x+5x = 360°

➝ 12x = 360°

➝ x = 360/12

➝ x = 30

So then the angles will be,

»» 1x = 1×30 = 30°

»» 2x = 2×30 = 60°

»» 4x = 4×30 = 120°

»» 5x = 5×30 = 150°

Do the angles of the quadrilateral are 30°,60°,120°,150°

Verification

➳ 1x+2x+4x+5x = 360°

➳ 30°+60°+120°+150° = 360°

➳ 90°+270° = 360°

➳ 360° = 360°

➳ LHS = RHS

Hence Verified!!

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Answer 2

AnSwEr :

• 30°
• 60°
• 120°
• 150°

Given :

• In a quadrilateral ABCD, a, b, c and d are in the ratio 1 : 2 : 4 : 5

To Find :

• Measure of each angle.

SoluTion :

★ Put x in the ratio

Now angles are

• x
• 2x
• 4x
• 5x

★ As we know that the sum of all angles of a quadrilateral is 360°

• According to question :

✩ x + 2x + 4x + 5x = 360°

→ 3x + 9x = 360°

→ 12x = 360°

→ x = 360°/12

→ x = 30°

Now,

Angles are :

• x => 30°
• 2x => (2 × 30)° => 60°
• 4x => (4 × 30)° => 120°
• 5x => (5 × 30)° => 150°

Hence, the angles are 30°, 60°, 120° and 150°.

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