Given

• Ratio of two linear angles = 7 : 5

To find

• The two angles

Solution

Let the two linear angles be 7x and 5x.

• First angle = 7x
• Second angle = 5x

As we know,

Sum of the linear angles = 180°

⟼ 7x + 5x = 180°

⟼ 12x = 180°

⟼ x = 180°/12

⟼ x = 15°

The value of x = 15°

The two linear angles :-

• First angle = 7x = 7 × 15° = 105°
• Second angle = 5x = 5 × 15° = 75°

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Let's verify :-

As we know, the sum of linear angles is equal to 180°. So, we will add both the angles and if their sum is equal to 180° then their values are right.

Put the value of x in eqn. 7x + 5x = 180°

• Taking LHS

⟼ 7 × 15° + 5 × 15°

⟼ 105° + 75°

⟼ 180°

LHS = RHS

Hence, verified.

Verified answer

Answer:

Ratio of two linear angles = 7:5

We already know that sum of two linear pair angles is 180°

So, Let the actual angles be multiplied by x

⇒ 7x + 5x = 180°

⇒ 12x = 180°

⇒ x° = 180°/12

⇒ x° = 15°

And now,

7(15) + 5(15) = 180°

⇒ 105° + 75° = 180°

∴ The angles are 105° and 75° respectively.

Thnx and have a nice day!

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