Question

the angles of a quadrilateral are in the rato 1:2:3:4. find all the angles​

Answer 1

Answer:

$x + 2x + 3x + 4x = 360 \\ 10x = 360 \\ x = 360 + 10 \\ x = 36 \\ \\ first \: angle = x \\ x = 36 \\ second \: angle \\ 2x = 2 \times 36 \\ 2x = 72 \\ \\ third \: angle \\ 3x = 3 \times36 \\ 3x = 96 \\ fourth \: angle \\ 4x = 4 \times 36 \\ 4x =$

Answer 2

$\textbf {\purple {\underline{Given:}}}$

• Angles of quadrilateral are in the ratio 1 : 2 : 3 : 4

$\textbf {\purple {\underline {To\:Find:}}}$

• All the angles of given quadrilateral.

$\huge\underline\green {\tt Solution:}$

Let the common factor of the angles be ' x '

So,

Angles will be - 1x , 2x , 3x and 4x

As we know, sum of all angles of quadrilateral is 360°

Now,

1x + 2x + 3x + 4x = 360°

➡ 10x = 360°

➡ x = $\dfrac {360}{10}$

•°• x = 36

Hence,

Angles are -

▪ 1x = 1 × 36 = 36°

▪ 2x = 2 × 36 = 72°

▪ 3x = 3 × 36 = 108°

▪ 4x = 4 × 36 = 144°

⭐ $\huge\mathscr\blue {Verification:}$

As stated above, the sum of all angles of quadrilateral is 360°

So,

36° + 72° + 108° + 144° = 360°

➡ 108° + 252° = 360°

➡ 360° = 360°

•°• L.H.S = R.H.S

Hence, Proved!