Question

Question 3. The angles of a quadrilateral are in the ratio of 2 : 3:5:8. Find the
measure of each angle.
Sol:​

Answer 1

Answer:

let the ratios be 2x,3x,5x,8x

now,

the sum of quadrilateral is 360

so,

2x+3x+5x+8x=360

18x=360

x= 360÷18=20

now,

2x= 2×20= 40

3x=3×20=60

5x=5×20=100

8x=8×20= 160

Answer 2

$\large\sf\underline{Given:-}$

• $\sf\:Ratio\:of\:angles\:=2:3:5:8$

$\large\sf\underline{To\:find:-}$

• $\sf\:Each\:angles\:of\:the\:quadrilateral$

$\large\sf\underline{Assumption:-}$

Let the four angles of the quadrilateral be :

• $\sf\:2x$

• $\sf\:3x$

• $\sf\:5x$

• $\sf\:8x$

$\large\sf\underline{Solution:-}$

We know,

$\large{\underline{\boxed{\mathrm\orange{Sum\:of\:all\:angles\:=360°}}}}$

$\sf\:So\:2x+3x+5x+8x=360°$

$\sf↦\:18x=360°$

$\sf↦\:x=\frac{360°}{18}$

$\sf↦\:x=20°$

Now substituting the value of x in all the angles :

$\sf\:1^{st}\:angle=2x$

$\sf↦\:1^{st}\:angle=2 \times 20°$

$\small{\underline{\boxed{\mathrm\pink{↦1^{st}\:angle=40°}}}}$

$\sf\:2^{nd}\:angle=3x$

$\sf↦\:2^{nd}\:angle=3 \times 20°$

$\small{\underline{\boxed{\mathrm\pink{↦2^{nd}\:angle=60°}}}}$

$\sf\:3^{rd}\:angle=5x$

$\sf↦\:3^{rd}\:angle=5 \times 20°$

$\small{\underline{\boxed{\mathrm\pink{↦3^{rd}\:angle=100°}}}}$

$\sf\:4^{th}\:angle=8x$

$\sf↦\:4^{th}\:angle=8 \times 20°$

$\small{\underline{\boxed{\mathrm\pink{↦4^{th}\:angle=160°}}}}$

• Thnku :)