Question

Let m∠COB = 50°30’, m∠AOB = 70° and m∠AOC = 20°30’. Could point C be in the interior of ∠AOB? Why?

PLEASE HELP SOON!!

Answer 1

No, Point cannot be inside ∠AOB.

Explanation:

Given information: m∠COB = 50°30’, m∠AOB = 70° and m∠AOC = 20°30’.

1 degree = 60 minutes

Using this conversion we get

m∠COB = 50°30’ = 50.5°

m∠AOB = 70°

m∠AOC = 20°30’ =20.5°

Let as assume C is in the interior of ∠AOB , then

m∠AOC+m∠COB=m∠AOB (angle addition postulate)

Taking LHS,

LHS = m∠AOC + m∠COB = 20.5° + 50.5° = 71°

Taking RHS,

RHS = m∠AOB = 70°

LHS ≠ RHS

It means our assumption is wrong.

Therefore, point C cannot be in the interior of ∠AOB.

Answer 2

Point cannot be inside ∠AOB

Explanation:

Consider the provided information.

m∠COB = 50°30’, m∠AOB = 70° and m∠AOC = 20°30’.

The angle addition postulate states that if C is in the interior of AOB , then

m∠AOC+m∠COB=m∠AOB

Substitute the respective values in above.

`20\°30'+50\°30'=70\°`

`30'+30'=60'=1\°` (∵ 1 degree is equal to 60 minutes )

`71\°=70\°`

Which is false.

Hence, point cannot be inside ∠AOB