Question

Two adjacent angle of a paralleogram are in the ratio 1:5. Find all the angle of the parallelogram

Answer 1

$\underline{\textbf{Answer}}$

$\underline{\textbf{Given That }}$

Two Adjacent Angles Of Parallelogram Are In The Ratio 1:5 , Had Now We Need To Find The all Angles...

$\underline{\textbf{Solution}}$

Let ABCD Be The Parallelogram And Angles = A , B , C , D ( Let
A And B Be The Given Adjacent Angle )

According To Question

$\mathbf{A\: : B \: = \: 1 \: : \:5}$

So Now Let

$\textbf{Let X Be The Constant Of Ratio }$

So We Have

$\angle$ A = 1x = X -- ( 1 )

$\angle$ B = 5x -- ( 2 )

Now According To Properties Of Parallelogram We Know That

$\textbf{Sum Of Adjacent Angles = 180\degree}$

Therefore We Have ➡️

A + B = 180° -- ( 3 )

That Is

X + 5x = 180°

6x = 180°

Now Taking 6 to RHS We Have ➡️

X = 180° ÷ 6

Therefore We Have

$\boxed{\mathbf{X\:= \: 30\degree}}$

So Now Putting Values Of X In EQ 1 And 2 We Have

$\angle$ A = X = 30°

$\angle$ B = 5x $\longrightarrow$ 5 × 30° = 150°

Now We Know That Opposite Angles Of Parallelogram Are Equal Therefore Here
$\angle$ A = $\angle$C , $\angle$ B = $\angle$D

So Now Putting Obtained Values of A And Be We Have ➡️

$\angle$ A = 30° = $\angle$ C

$\angle$ B = 150° = $\angle$ D

$\underline{\textbf{Hence The Required Answer Is }}$

$\boxed{\mathbf{\angle A\: = \:30 \degree\:,\:\angle\: C\:= \:30 \degree\: , \: \angle B \: = \: 150 \degree\:And \: \angle D\: =\: 150 \degree}}$