Question

One angle of a quadrilateral is 72°. The others are in the ratios 1 : 2 : 3. Find them.

Answer 1

Define x:

Let x be the constant ratio

Ratio : 1x  : 2x : 3x : 4x

Solve x:

1x + 2x + 3x + 4x = 10x

10x = 360

x = 36

Find each angle:

x = 36°

2x = 2(36) = 72°

3x = 3(36) = 108°

4x = 4(36) = 144°

Answer: The angles are 36°, 72°, 108° and 144°

Answer 2

<1=72°

Let the unknown angle be z.

Given ratio : 1:2:3

So, 72°+z+2z+3z=360° (Sum of all the angles in a quadrilateral is 360°)

72°+6z=360°

6z=360°-72°

z=288°/6

z=48°

<1=72°

<2=48°

<3=96°

<4=192°

Hope you appreciate the answer !

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