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.

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation: