Question

In the adjoining figure, it is given that ab || cd,

∠boa = 108 and ∠ocd = 120, then ∠aoc = ____.

Answer 1

Answer:

Option (c) is correct. ∠AOC is 132° .

Step-by-step explanation:

Given :

• ∠BAO is 108°.
• ∠OCD is 120°.

To find :

• Value of ∠AOC.

Solution :

Construction :

• Draw a line PO, Parallel to both AB and DC.

We know,

✿ Sum of two interior angles lie between two parallel lines and on same side of the transversal are equal to 180° or we can say this property "Co- interior angles" .

Here, AB, OP and DC are parallel lines and AO and OC are transversals .

So,

$\implies$ ∠AOP + ∠BAO = 180°.

$\implies$ ∠AOP + 108° = 180°

$\implies$ ∠AOP = 180° - 108°

$\implies$ ∠AOP = 72°

∠AOP is 72°.

Similarly,

$\implies$ ∠POC + ∠OCD = 180°

$\implies$ ∠POC + 120° = 180°

$\implies$ ∠POC = 180° - 120°

$\implies$ ∠POC = 60°

∠POC is 60°.

Now,

$\implies$ ∠AOC = ∠AOP + ∠POC

$\implies$ ∠AOC = 72° + 60° [As we find above]

$\implies$ ∠AOC = 132°

Therefore,

Option (c) is correct.

∠AOC is 132°.

Answer 2

Option c) 132° is the Correct Answer.

EXPLANATION :

Given :

∠BAO is 108°

∠OCD is 120°

To Find :

Value of ∠AOC.

Solution :

CONSTRUCTION :

Draw a line PO, Parallel to both AB and DC.

We know that,

⬟ Sum of two interior angles lie between two lines and same side of transversal are equal to 180° or we can say "Co - interior angles" .

⇒ ∠AOP + ∠BAO = 180°

⇒ ∠AOP + 108° = 180°

⇒ ∠AOP = 180° - 108°

⇒ ∠AOP = 72°

SIMILARLY,

⇒ ∠POC + ∠OCD = 180°

⇒ ∠POC + 120° = 180°

⇒ ∠POC = 180° - 120°

⇒ ∠POC = 60°

THEN,

⇒ ∠AOC = ∠AOP + ∠POC

⇒ ∠AOC = 72° + 60°

⇒ ∠AOC = 132°

FINAL ANSWER :

The Value of ∠AOC is 132° .

∴ Option (c) is the Correct Answer.