Question

If two adjacent angles of a parallelogram are (7x - 10) and (8x - 5), then the ratio of these angles is​

Answer 1

Answer :

• The ratio of their angles are 9 : 11.

Step-by-step explanation ::

To Find :-

• The ratio of the angles

Solution ::

Given that,

• The two adjacent angles of parallelogram are ( 7x - 10 )° and ( 8x - 5 )°

Figure :-

• Refer the attachment.

Therefore, the angles are ::-

As we know that,

Adjacent angles of parallelogram are supplementary [ 180° ],

Therefore, ( 7x - 10 )° + ( 8x - 5 )° = 180°,

➭ 7x - 10 + 8x - 5 = 180

➭ 7x + 8x - 10 - 5 = 180

➭ 15x - 15 = 180

➭ 15x = 180 + 15

➭ 15x = 195

➭ x = 195/15

➭ x = 13

The value of x is 13.

The angles are ::

➭ 7x - 10

➭ 7*13 - 10 = 91 - 10 = 81°

➭ 8x - 5

➭ 8*13 - 5 = 104 - 5 = 99°

The angles are 81° and 99°.

According the question,

The ratio of the angles are -:

➭ 81 : 99

➭ 27 : 33

➭ 9 : 11

The ratio of their angles are 9:11.

Answer 2

Question:

If two adjacent angles of a parallelogram are (7x - 10) and (8x - 5), then the ratio of these angles is ?.

To find:

• Ratio of adjacent angles

Given:

• 1 adjacent angle = (7x - 10)

• 2 adjacent angle = (8x - 5)

Solution:

To find ratio , we should know value of x

We know:

$\boxed{ \text{Sum of adjacent angles of parallelogram = 180 \degree}}$

By using this identity we can find value of x

$\dashrightarrow\sf Sum \: of \: adjacent \: angles \: of parallelogram \: = 180 \degree \\ \\ \dashrightarrow\sf(7x - 10) + (8x - 5) = 180 \degree \\ \\ \dashrightarrow\sf7x - 10 + 8x - 5 = 180 \degree \\ \\ \dashrightarrow\sf \{7x + 8x \} + \{ - 10 - 5 \} = 180 \degree \\ \\ \dashrightarrow\sf15x - 15 = 180 \degree \\ \\ \dashrightarrow\sf15x = 180 + 15 \\ \\ \dashrightarrow\sf15x = 195 \degree \\ \\ \dashrightarrow\sf{}x = \frac{195}{15} \degree \\ \\ \dashrightarrow\sf x = \cancel \dfrac{195}{5} \degree \\ \\ \dashrightarrow \underline{ \boxed{\sf x = 13}}$

Let's Verify value of x

Verification:

$\dashrightarrow\sf(7x - 10) + (8x - 5) = 180 \degree$

put value of x in this equation:

$\dashrightarrow\sf(7 \times 13 - 10) + (8 \times 13- 5) = 180 \degree \\ \\ \dashrightarrow\sf(91 - 10) + (104 - 5) = 180 \degree \\ \\ \dashrightarrow\sf81+ 99 = 180 \degree \\ \\ \dashrightarrow \underline{\boxed{\sf 180 \degree = 180 \degree }}$

LHS = RHS

Hence verified!

Now Let's find value of 1 angles

• 7x - 10
• 7 × 13 - 10
• 91 - 10
• 81°

To find 2 angle:

• 8x - 5
• 8 × 13 - 5
• 104 - 5
• 99°

Now Let's find ratio:

$\dashrightarrow \sf Ratio = \dfrac{7x - 10 \degree}{8x - 5} \\ \\ \dashrightarrow \sf Ratio = \dfrac{81}{99} \\ \\ \dashrightarrow\sf Ratio = \dfrac{9}{11} \\ \\ \dashrightarrow \underline{\boxed{\sf Ratio = 9: 11}}$

$\therefore \underline{ \sf{Ratio\:of\:Parallelogram =9 : 11 }}$