Question

the angles of a quadrilateral are 2xdegree, 3x degree, 2(2x+1)and 5(x+3)

1=find x
2= find each angle
​

Answer 1

$\large\sf\underline{✰\:Given}$

$\sf\:Four\:angles\:of\:a\: quadrilateral$

• $\sf\:2x°$

• $\sf\:3x°$

• $\sf\:2(2x+1)°$

• $\sf\:5(x+3)°$

$\large\sf\underline{✰\:To\:find}$

• The value of x

• Each angle of quadrilateral

$\large\sf\underline{✰\:Solution}$

We know ,

$\tt\red{Sum\:of\:Angles\: in \:a\: quadrilateral=360°}$

So following that we get :-

$\sf⇥\:2x+3x+2(2x+1)+5(x+3)=360°$

$\sf⇥\:2x+3x+4x+2+5x+15=360°$

$\sf⇥\:2x+3x+4x+5x=360°-2-15$

$\sf⇥\:14x=358°-15$

$\sf⇥\:14x=358°-15$

$\sf⇥\:14x=343°$

$\sf⇥\:x=\frac{343°}{14}$

$\sf⇥\:x=24.5°$

$\huge\fbox\red{⇝x = 24.5°}$

Now substituting the value of x in four angles :

$\sf⇨\:2x°$

$\sf⇨\:2 \times 24.5$

$\large\fbox\pink{⇨49°}$

$\sf\:⇨3x°$

$\sf⇨\:3 \times 24.5$

$\large\fbox\pink{⇨73.5°}$

$\sf⇨\:2(2x+1)°$

$\sf⇨\:4x+2$

$\sf⇨\:4 \times 24.5 +2$

$\sf⇨\:98+2$

$\large\fbox\pink{⇨100°}$

$\sf⇨\:5(x+3)°$

$\sf⇨\:5x+15$

$\sf⇨\:5 \times 24.5 +15$

$\sf⇨\:122.5+15$

$\large\fbox\pink{⇨137.5°}$

$\sf✰\:So\:the\:four\:angles\:of\:a\:quadrilateral\:are$

$\tt\pink{⇨49°}$

$\tt\pink{⇨73.5°}$

$\tt\pink{⇨100°}$

$\tt\pink{⇨137.5°}$

$\sf✰\:Sum\:of\:them\:are$

$\tt\red{⟹\:49°+73.5°+100°+137.5°}$

$\tt\red{⟹\:360°}$

Hope it helps :)