Question

two adjacent angles of a parallelogram are in ratio 1 : 5. Find all the angles of a parallelogram​

Answer 1

Given :

• Ratio of two adjacent angles of a parallelogram = 1:5

Have to find :

• Find all angles of a parallelogram.

Solution :-

Note :- Opposite angles of a parallelogram are equal

So, lets we consider the angles be ' 1x ' and ' 5x '

⠀$\implies$x + 5x = 180°

⠀⠀⠀⠀⠀$\implies$6x = 180°

⠀⠀⠀⠀⠀ $\implies$x = 180° ÷ 6

⠀⠀⠀⠀⠀ $\implies$x = 30°

⠀

Now, we got " x " → 30°

First Angle be 1x :

⇒ 1x

⇒ 1 × (30°)

⇒ 30°

Second angle be 5x :

⇒ 5x

⇒ 5 × (30°)

⇒ 150°

As I mentioned above , Opposite angles be equal.

Thus ,the angles of a paralellogram are 30°, 150°, 30° and 150° respectively.

Answer 2

$\Large{\underbrace{\sf{\purple{Required\:Solution:}}}}$

Given thαt,

• Two αdjαcent αngles of α pαrαllelogrαm αre in rαtio 1:5.

◾️We hαve to find αll the αngles of the pαrαllelogrαm.

___________

To do so,

Let the αngles be 1x αnd 5x.

$\large\star{\boxed{\sf{\purple{ Sum\:of\:two\:adjacent\:angles = 180^{\circ}}}}}$

According to the question,

$\longrightarrow{\sf{ x+5x = 180^{\circ}}}$

$\longrightarrow{\sf{ 6x = 180^{\circ}}}$

$\longrightarrow{\sf{ x = \dfrac{180^{\circ}}{6}}}$

$\longrightarrow{\sf{ x = 30^{\circ}}}$

Therefore, the αngles αre —

$\implies{\sf{ x = {\purple{30^{\circ}}}}}$

$\implies{\sf{ 5x = {\purple{150^{\circ}}}}}$

In α pαrαllelogrαm, opposite αngles αre equαl.

Therefore, the meαsure of αll αngles αre 30°,150°,30° αnd 150° respectively.

And we αre done! :D

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