Question

The angles of an quarilateral are in the ratio of 1:2:3:4 hence the measurement of smallest angle is. Answer

Answer 1

GIVEN:-

The angles of an quarilateral are in the ratio of 1:2:3:4.

TO FIND:-

The measurement of smallest angle.

SOLUTION:-

We know that the sum of all angles of a quadrilateral is 360°.

Therefore,

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

According to the question,

$\large\Rightarrow{\sf{x+2x+3x+4x=360}}$

$\large\Rightarrow{\sf{10x=360}}$

$\large\Rightarrow{\sf{x=\dfrac{360}{10}}}$

$\large\Rightarrow{\sf{x=\dfrac{36\cancel{0}}{1\cancel{0}}}}$

$\large\therefore\boxed{\sf{x=36}}$

So,

The angles are:-

1. x = 36°
2. 2x = 2 × 36 = 72°
3. 3x = 3 × 36 = 108°
4. 4x = 4 × 36 = 144°

Now let's verify it:-

$\large\Rightarrow{\sf{36+72+108+144=360}}$

$\large\Rightarrow{\sf{360\degree=360\degree}}$

$\large\therefore\boxed{\sf{LHS=RHS}}$

$\large{\pink{\underline{\boxed{\therefore{\sf{\pink{The\:smallest\:angle\:is\:36\degree.}}}}}}}$

Answer 2

Solution

Given ,

• the angle of a quadrilateral are in ratio of 1:2:3:4 .

To find ,

• find the measurement of each of the angle

Now ,

According to the given question ,

We know that ,

• the sum of all angles of a quadrilateral is 360° .
• let the ratio Be in "X"

So , it will form a equation , 1x+2x+3x+4x=360

now solving this equation we Get ;

=> 1x + 2x +3x +4x =360°

=> 10x = 360°

=> x = 360/10

=> x = 36°

So ,

• the value of 1 is 36 degree .

now a measure of all angles ,

• 1x = 1×36° =36°
• 2x = 2×36° = 72°
• 3x= 3×36° = 108°
• 4x = 4×36°= 144°

Each angel is 36°,72°,108°,144° .

Verification

• to do verification we have to just add all the numbers and check that the sum will be 360 degree or not .

=> 36°+72°+108°+144°=360°

=> 360°=360°

Hence , LHS = RHS