Question

the four angles of a quadrilateral are in the ratio of 2:3:5:8.find the angles​

Answer 1

Answer:

we know that sum of angles of quadrilateral is 360°

let angles be 2x,3x,5x,8x

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

18x=360

x=20

2x=2×20=40

5x=100

8x=160

Answer 2

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Given:

Four angles of quadrilateral are in ratio 2:3:5:8.

To Find :

The actual measure of all four angle.

Solution:

let the measure of angles of the given quadrilateral be

$(2x) \degree \: , \: (3x)\degree \: , \: (5x)\degree \: and \: (8x)\degree$

we know that ,

the sum of the angles of a quadrilateral is 360 °

$\therefore \: 2x + 3x + 5x + 8x = 360 \degree \: \\ \implies \: 18x = 360\degree \: \\ x = \cancel \frac{360\degree}{18} \\ \\ x = 20\degree \:$

so, the measure of all angles of the given quadrilateral are given below

$(2 \times 20)\degree = 40\degree \\ (3 \times 20)\degree = 60\degree \\ (5 \times 20)\degree = 100\degree \\ (8 \times 20)\degree = 160\degree$