Question

The angle A,B,C, and D of a quadrilateral ABCD are in the ratio 1:2:3:4 find the measure of each angle

Answer 1

Answer:

36 , 72 , 108 , 144

Step-by-step explanation:

Sum of all angles of quadrilateral is 360

Let the angles be x , 2x , 3x and 4x

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

==: 10x = 360

==: x = 36

Angles = x = 36

            = 2x = 72

            = 3x = 108

            = 4x = 144

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Answer 2

Step-by-step explanation:

Express the given ratios is the trem of x

So,

angle A = 1x

angle B = 2x

angle C = 3x

angle D = 4x

As we know that,

sum of all four angles of a quadrilateral = 360°

Therefore,

1x + 2x + 3x + 4x = 360°

10x = 360°

x = 36

Now put the value of x in the ratios

angle A = 1x

= 1 × 36

= 36°

angle B = 2x

= 2 x 36

= 72°

angle C = 3x

= 3 x 36

= 108°

angle D = 4x

= 4 x 36

= 144°

Thus Angle A = 36°

Angle B = 72°

Angle C = 108°

Angle D = 144°