Question

13•in figure,AOB and COD are straight lines. ¡)Find the value of a and b​

Answer 1

Answer:

• Value of a is 10°.
• Value of b is 25°.

Step-by-step explanation:

To find :

• Value of a and b.

Solution :

By Vertically opposite angles:

• ∠AOC = ∠DOB

⇒ 3a° + 40° = a° + 60°

⇒ 3a° - a° = 60° - 40°

⇒ 2a° = 20°

⇒ a° = 20°/2

⇒ a° = 10°

∴ Value of a is 10°.

We know,

Sum of all angles forms on straight line is equal to 180° or we can say linear pair.

So,

• ∠AOC + ∠BOC = 180°

⇒ 3a° + 40° + 4b° + 10° = 180°

• Put a° = 10°.

⇒ 3 × (10°) + 40° + 4b° + 10° = 180°

⇒ 30° + 40° + 4b° + 10° = 180°

⇒ 70° + 4b° + 10° = 180°

⇒ 80° + 4b° = 180°

⇒ 4b° = 180° - 80°

⇒ 4b° = 100°

⇒ b° = 100°/4

⇒ b° = 25°

∴ Value of b is 25°.

Answer 2

❍ Given that, AOB and COD are straight lines in this figure and we can see that,

• 3a + 40° and a + 60° are vertically opposite angles
• 4b + 10° and a + 60° are supplementary angles

⠀ ━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀

As we know that,

•  Vertically opposite angles are equal and sum of supplementary angles is 180°.

Finding the value of a :-

$\sf : \; \implies$  3a° + 40° = a° + 60°  

$\sf : \; \implies$  3a° - a° = 60° - 40°

$\sf : \; \implies$ 2a° = 20°

$\sf : \; \implies$ a = 20°/2

$\sf : \; \implies$ a = 10

Henceforth,  according to this figure the value of a is 10

⠀ ━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀

Finding the value of b :-

$\sf : \; \implies$ a° + 60° + 4b° + 10° = 180°

$\sf \bigstar$ [ putting value of a which we've calculated above ]

$\sf : \; \implies$ 10° + 60° + 4b° + 10° = 180°

$\sf : \; \implies$ 4b° + 80° = 180°

$\sf : \; \implies$ 4b = 180° - 80°

$\sf : \; \implies$ 4b = 100°

$\sf : \; \implies$ b = 100°/4

$\sf : \; \implies$ b = 25

⠀ ━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀

Henceforth,  according to this figure the value of b is 25