Let m∠cob = 50°30’, m∠aob = 70° and m∠aoc = 20°30’. could point c be in the interior of ∠aob? why?

No, Point cannot be inside ∠AOB.

Step-by-step 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.

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt