Question

A camp ground site is in the shape of a quadrilateral. If the angles formed between the sides of the ground are in the ratio 1 : 2 : 3 : 4, the angles measure ___________. 36°, 72°, 108°, 144° 40°, 80°, 120°, 160° 25°, 50°, 75°, 100° 30°, 60°, 90°, 120°

Answer 1

Step-by-step explanation:

let the angle be x.

x+2x+3x+4x=360°(sum of quadrilateral is 360°)

10x=360°

x=360/10

x=36

so measure of angles are :

x= 36

2x= 2*x = 2*36=72

3x=3*x=3*36=108

4x=4*x=4*36=144

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Answer 2

Answer:

$\qquad\boxed{ \sf{ \: The\:angle\:measure\:are \: 36 \degree, \: 72 \degree, \: 108 \degree, \: 144 \degree \: }}$

Step-by-step explanation:

Given that,

A camp ground site is in the shape of a quadrilateral and the angles formed between the sides of the ground are in the ratio 1 : 2 : 3 : 4.

Let assume that angle of a quadrilateral are x, 2x, 3x, 4x respectively.

We know, sum of all interior angles of a quadrilateral is 360°.

So,

$\sf \: x + 2x + 3x + 4x = 360 \degree$

$\sf \: 10x = 360 \degree$

$\sf\implies \sf \: x = 36 \degree$

Thus, angles of a quadrilateral are

$\sf \: x = 36 \degree$

$\sf \: 2x = 2 \times 36 = 72 \degree$

$\sf \: 3x = 3\times 36 = 108 \degree$

$\sf \: 4x = 4\times 36 = 144 \degree$

Hence,

$\sf\implies The\:angle\:measure\:are \: 36 \degree, \: 72 \degree, \: 108 \degree, \: 144 \degree$

$\rule{190pt}{2pt}$

Additional information

Sum of all interior angles of a convex polygon of n sides is

$\sf \:\qquad\boxed{ \sf{ \:(2n - 4) \times 90\degree \: \: }}$

For a regular polygon of n sides, we have a relationship

$\qquad\boxed{ \sf{ \:Exterior \: angle \: = \: \frac{360\degree}{n} \: }}$

$\qquad\boxed{ \sf{ \:n \: = \: \frac{360\degree}{Exterior \: angle} \: }}$

The smallest interior angle of a regular polygon is 60°.

The largest exterior angle of a regular polygon is 120°.