Question

the angles of quadrilateral are in the ratio 4:5:10:11 find the angles​

Answer 1

Explanation:

Let the angles be 4x , 5x , 10x and 11x

As we know that sum of all internal angle of a quadrilateral is 360°

so

4x + 5x + 10x + 11x = 360°

30x = 360°

X = 12°

Now

First angle = 4x = 4× 12 = 48°

Second Angle = 5x = 5×12= 60°

Third angle = 10x = 10× 12 = 120°

fourth angle = 11x = 11×12 = 132°

Hence the required angles are 48° , 60° , 120° and 132°

Answer 2

$\large{\underline{\underline{\pmb{\sf{\spadesuit\:Question:}}}}}$

The angles of a quadrilateral are in the ratio: 4:5:10:11. Find all the angles.

$\large{\underline{\underline{\pmb{\sf{\spadesuit\:Assume:}}}}}$

$\implies\sf{First\:angle = 4x}$

$\implies\sf{Second\:angle = 5x}$

$\implies\sf{Third\:angle = 10x}$

$\implies\sf{Fourth\:angle = 11x}$

$\large{\underline{\underline{\pmb{\sf{\spadesuit\:Solution:}}}}}$

We know that sum of all the angles of the quadrilateral is 360°. This implies that:

$\pink{\boxed{\implies{\sf{\angle{A}+\angle{B}+\angle{C}+\angle{D} = 360\degree}}}}\bigstar$

$\implies\sf{4x+5x+10x+11x = 360\degree}$

$\implies\sf{30x = 360\degree}$

$\implies\sf{x = \dfrac{360}{30}}$

$\large{\red{\boxed{\implies{\sf{x=12}}}}}\bigstar$

Hence, the angles are:

$\implies\sf{First\:angle = 4 \times 12 = 48\degree}$

$\implies\sf{Second\:angle = 5 \times 12 = 60\degree}$

$\implies\sf{Third\:angle = 10 \times 12 = 120\degree}$

$\implies\sf{Fourth\:angle = 11 \times 12 = 132\degree}$