Question

The angles of a quadrilateral are in the ratio 3 : 4 : 5 : 6. Find all the angles of the quadrilateral.

​

Answer 1

Answer:

In a quadilateral the angles add up to

360

o

Let's call the angles

3

x

,

4

x

,

5

x

and

6

x

Then:

3

x

+

4

x

+

5

x

+

6

x

=

360

→

18

x

=

360

→

x

=

20

Then the angles are

60

o

,

80

o

,

100

o

and

120

o

(because

3

⋅

20

=

60

etc)

Check:

60

+

80

+

100

+

120

=

360

Step-by-step explanation:

please Mark me as brainiest

Answer 2

Answer :-

• The angles of the quadrilateral are 60°, 80°, 100° and 120°.

Given :-

• The angles of a quadrilateral are in the ratio 3 : 4 : 5 : 6.

To find :-

• All the angles of the quadrilateral.

Step-by-step explanation :-

• Here, it has been given that the angles of a quadrilateral are in the ratio 3 : 4 : 5 : 6. We have to find all it's angles.

• The angles of the quadrilateral are in the ratio 3 : 4 : 5 : 6, so let them be 3x, 4x, 5x and 6x respectively.

We know that :-

$\underline{ \boxed{\sf Sum \: of \: all \: angles \: in \: a \: quadrilateral = 360^{\circ}}}$

-----------------------------

Hence,

$\rm3x + 4x + 5x + 6x = 360$

Adding 3x, 4x, 5x and 6x,

$\rm18x = 360^{\circ}$

Transposing 18 from LHS to RHS, changing it's sign,

$\rm x = \dfrac{ \: \: 360^{\circ}}{18}$

Dividing 360° by 18,

$\overline{ \boxed{\rm x = 20^{\circ}}}$

-----------------------------

Hence, all the angles are as follows :-

$\bf3x = 3 \times 20^{\circ} = 60^{\circ}$

$\bf4x = 4 \times 20^{\circ} = 80^{\circ}$

$\bf5x = 5 \times 20^{\circ} = 100^{\circ}$

$\bf6x = 6 \times 20^{\circ} = 120^{\circ}$