Question

The angles of a quadrilateral given as in the ration 1:2:3:4 Find all the angles​

Answer 1

Answer:

x = 36°

2x = 2 × 36 = 72°

3x = 3 × 36 = 108°

4x = 4 × 36 = 144°

Step-by-step explanation:

1x + 2x + 3x + 4x = 360

10x = 360

x = 360/10

x = 36

Answer 2

Question :-

• The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find all the angles.

Answer :-

• The angles of the quadrilateral are 36°, 72°, 108° and 144°.

To find :-

• All the angles of the quadrilateral.

Solution :-

• Here, we have to find the angles of a quadrilateral using the ratio given to us.

Let :-

• The angles of the quadrilateral be x, 2x, 3x and 4x as they are in the ratio 1 : 2 : 3 : 4.

We know that :-

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

Which means that :-

• The sum of x, 2x, 3x and 4x is 360°.

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

Therefore,

$\longmapsto\tt x + 2x + 3x + 4x = 360^{ \circ}$

$\longmapsto\tt10x = 360^{ \circ}$

$\longmapsto\tt x = \dfrac{\:\:360^{ \circ}}{10}$

$\longmapsto\overline{ \boxed{ \tt x = 36^{ \circ}}}$

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

Hence, the angles of the quadrilateral are as follows :-

$\bf x = 36^{ \circ}$

$\bf2x = 2 \times 36^{ \circ} = 72^{ \circ}$

$\bf3x = 3 \times 36^{ \circ} = 108^{ \circ}$

$\bf4x = 4 \times 36^{ \circ} = 144^{ \circ}$

________________________________