Question

one angle of a quadrilateral is a right angle and remaining three angle are in the ratio of 2 ratio 3 ratio 4 determine the measure of each of them​

Answer 1

Solution:-

One angle of Quadrilateral is 90° (given)

Let the Ratio of angles be 2x,3x,4x

As we know that in a Quadrilateral the sum of all angles is 360° .

So , put the value we get

→ 2x +3x +4x +90° = 360°

→ 2x +3x +4x = 360° -90°

→ 9x = = 270°

→ x = 270°/9

→ x = 30°

Put the value of x in the given ratio we get

→ 2x = 2×30° = 60°

→ 3x = 3×30 = 90°

→ 4x = 4×30 = 120°

Therefore the remaining angles of the Quadrilateral is 60° , 90° & 120°

Answer 2

Solution

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Given,

• one angle of a quadrilateral is 90 degree
• and the remaining three angles are in ratio 2:3:4

To find ,

• the measure of each angle of them

We know that ,

• the sum of all angles of a quadrilateral is 360 degree .
• also we know that there are four sides of a quadrilateral .

So,

$\bold{2 x + 3x + 4x + 90 \degree = 360 \degree}$

now solving this equation we get ;

$= > 2x + 3x + 4x = 360 - 90$

$= > 9x = 270$

$= > x = \frac{270}{9}$

$\bold{ = > x = 30 \degree}$

Now,

measuring of each angle ;

$\bold{2x = 2 \times 30 = 60 \degree}$

$\bold{3x = 3 \times 30 = 90 \degree}$

$\bold{4x = 4 \times 30 = 120 \degree}$

So, the measure of each angle is 60 degree , 90 degree and 120 degree .

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