Question

THE measure of the angles of the quadrilateral ABCD are in the ratio 2:3;:4:1. Find the measure of each angle
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Answer 1

The questions is that the measure of each angle of a quadrilateral ABCD are in the ratio of 2:3:4:1 . All of them are in different forms so we need a same variable x and multiply it with all the ratios given .

• 2 × x = 2x
• 3 × x = 3x
• 4 × x = 4x
• 1 × x = 1x

We know that the sum of all angles of quadrilateral according to the angle sum property is 360° .

Thus ,

➜ 2x + 3x + 4x + 1x = 360°

➜ 5x + 5x = 360°

➜ 10x = 360°

➜ x = 360/10

➜ x = 36°

Now , when we multiply 36 with all the ratios we get the angles . Each angle is :

2 × 36 => 72°

3 × 36 => 108°

4 × 36 => 144°

1 × 36 => 36°

For verification if we add all the angles we must and get 360°

72 + 108 + 144 + 36 = 360

360 = 360

LHS = RHS

Answer 2

Answer:

$\huge \bf \: given$

• Measure of quardilateral ABCD (in ratio) = 2:3:4:1

$\huge \bf \: to \: find$

Measure of each angle

$\huge \tt \: answer$

Let the angle of quardilateral ABCD be x

Sum of ratio = 2x + 3x + 4x + 1x = 10x

As we know that sum of all angle in quardilateral is 360⁰

$10x = 360 \degree$

$x = \frac{360}{10}$

$x = 36$

So, the value of x is 36

Then

$2x = 2 \times 36 = 72 \degree$

$3x = 3 \times 36 = 108 \degree$

$4x = 4 \times 36 = 144 \degree$

$1x = 1 \times 36 = 36 \degree$

Verification

$72 \degree \: + 108\degree + 144\degree + 36\degree = 360\degree$

$180\degree + 180\degree = 360\degree$

$360\degree = 360\degree$

$LHS \: = RHS \:$