Question

In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1: 2:4:5. Find the measure
of each angle of the quadrilateral.​

Answer 1

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Given

• Ratio of angles = 1 : 2 : 4 : 5

To Calculate

• Angles of quadrilateral

Solution

Let the angles be x, 2x, 4x and 5x

According to question,

$\bf \implies x + 2x + 4x + 5x = 360°$

$\bf \implies 12x = 360°$

$\bf \implies x = 360°/ 12 \div 15$

$\bf \implies x = 30° \degree$

• x = 1 × 30 = 30°
• 2x = 2 × 30= 60°
• 4x = 4 × 30 = 120°
• 5x = 5 × 30 = 150°

Therefore, angles of triangle are 30°, 60°, 120° and 150°.

Answer 2

Answer:

∠A:∠B:∠C:∠D=1:2:3:4

So, let ∠A=x,∠B=2x,∠C=3x,∠D=4x

Therefore, by angle sum property of quadrilateral,

x+2x+3x+4x=360

10x=360

x=36

o

Hence,

∠A=36

o

,∠B=72

o

,∠C=108

o

,∠D=144

o

.

Step-by-step explanation:

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