Question

In a parallelogram, adjacent angles are in the ratio 1:4, then the sum of all its interior angles is?

Answer 1

Answer:

obviously it will be 360°

Step-by-step explanation:

sum of all the angles of quadrilateral is 360°

Answer 2

Question:

In a parallelogram, adjacent angles are in the ratio 1:4, then the sum of all its interior angles is?

To find:

To find the sum of its interior angles.

Answer:

$\underline{ \: \underline{ \: \sf\pink{\bold{Sum \: of \: interior \: angles \: is \: 180°}} \: } \: }$

Given:

Adjacent angles are in ratio 1 : 4 .

$Adjacent \: angles \: are \: x \: and \: 4x$

Step-by-step explanation:

Let the angle be x and 4x .

Let the parallelogram be ABCD.

We know that in parallelogram,

Adjacent angles of a Parallelogram are Supplementary.

$\boxed{Sum \: of \: adjacent \: angles=180°}$

$x + 4x = 180°$

$5x = 180°$

$\boxed{x = 36°}$

$x = 36°$

$4x = 4(36) = 144°$

$\therefore The \: angles \: are \: 36°,144°$

Now, to find the sum of all its interior angles

$36° + 144° = 180°$

$\therefore Sum \: of \: interior \: angles=180°$

Rule used:

$\bigstar \: Sum \: of \: adjacent \: angles=180°$

★ Adjacent angles of a Parallelogram are Supplementary.