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

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

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

1. Answer: 1 : 3

Step-by-step explanation:

### 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

### =1:3ANS.

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2. 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

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