Question

If two adjacent angles of a parallelogram are (5x-5) and (10x+35), then the ratio of these angle is ​

Answer 1

Answer :

1 : 3

Explanation :

In a parallelogram,

Two adjacent angles are $(5x - 5)$ and $(10x + 35)$

Find the ratio of these angles.

Let's calculate the angles first.

We know that, the adjacent angles of a parallelogram are supplementary which will add up to 180°

$\therefore (5x - 5) + (10x + 35) = 180^{\circ}$

Solving for $\boldsymbol x$

${ \implies \: (5x - 5) + (10x + 35) = 180^{ \circ} }$

$\implies \:5x - 5 + 10x + 35 = {180}^{ \circ}$

$\implies \:15x + 30 = {180}^{ \circ}$

$\implies \:15x = {180}^{ \circ} - {30}^{ \circ}$

$\implies \:15x = {150}^{ \circ}$

$\implies \:x = \frac{150}{15}$

$\implies \:x = {10}^{ \circ}$

${ \underline{ \sf{\therefore{The \: value \: of \: \boldsymbol{x} \: is \: {10}^{ \circ} }}}}$

Hence, the angles are :

• $(5x - 5) = \sf 5(10) - 5 = \blue{45^{\circ}}$
• $(10x + 35) = \sf 10(10) + 35 = \blue{135^{\circ}}$

Forming in ratio :

→ 45 : 135

→ 9 : 27

→ 1 : 3

Required ratio = 1 : 3

Answer 2

Answer: 1 : 3

Step-by-step explanation:

Given: In a parallelogram,

First adjacent angle = (5x-5)

Second adjacent angle = (10x+35)

To Find: The ratio of these angles.

Solution:

We know that in a parallelogram the sum of the adjacent angles is always equal to 180°.

(5x-5)+(10x+35) = 180

=> 5x +10x +35-5 = 180

=> 15x + 30 = 180

=> 15x = 180-30

=> 15x = 150

x = 150/15 = 10

Now,

The ratio of these angles =

$= \frac{first \: angle}{second \: angle} \\ = \frac{(5x - 5)}{(10x + 35)} \\ = \frac{5(x - 1)}{5(2x + 7)} \\ = \frac{(x -1)}{(2x + 7)} \\ = \frac{(10 - 1)}{(2 \times 10 + 7)} \\ = \frac{9}{20 + 7} \\ = \frac{9}{27} \\ = \frac{1}{3}$

= 1 : 3 ANS.