Question

Two adjacent angle of a parrlelogram are in the ratio 4:5.find the measure of all the angles of a parrlelogram.

Answer 1

given the ratio between the two adjacent angles of a parallelogram is 4 : 5

let the two adjacent angles of the paralelegram be 4x and 5x respectively.

we know that,

» sum of two adjacent angles in a parallelogram = 180°

➡ 4x + 5x = 180°

➡ 9x = 180°

➡ x = 180/9

➡ x = 20°

therefore the two adjacent angles are :-

• 4x = 4 × 20 = 80°

• 5x = 5 × 20 = 100°

now, also the opposite angles of a parallelogram is same. it's one of it's properties. opposite angles are same in a parallelogram.

hence, all the angles of the parallelogram are 80°, 100°, 80° and 100°

Answer 2

• Let angles of parallelogram be M.

» Two adjacent angle of a parallelogram are in the ratio 4:5.

So, one angle = 4M and other angle = 5M.

(Refer the attachment for figure)

In figure ABCD is a parallelogram such that..

$\angle{A}$ = $\angle1$, $\angle{B}$ = $\angle2$, $\angle{C}$ = $\angle3$ and $\angle{D}$ = $\angle4$.

Now..

$\angle1$ = 4M and $\angle2$ = 5M

We know that ..

Sum of adjacent sides of parallelogram is 180°

=> $\angle1$ + $\angle2$ = 180°

=> 4M + 5M = 180°

=> 9M = 180°

=> M = 180/9

=> M = 20°

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One angle = 4M = 4(20) = 80°

and

Other angle = 5M = 5(20) = 100°

Similarly, for $\angleC$ and $\angleD$ we get the same result.

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80°,100°, 80° and 100° are the angles of a parallelogram.

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