I really need help!!!!!!!!!!!!!!!

The reason given on the line of interest is "substitution," so the problem boils down to determining what was substituted for what. The previous statement says ...

AOC + COB = 90

and the first part of the statement we're to complete has BOC + ___.

We see from the given statements that m∠AOC = m∠BOC + 30°, so it appears that is the substitution that has been made: AOC has been replaced by BOC + 30.

This means the first blank is filled with 30.

__

The second part of the previous statement is ...

AOC + COB = 90

so we believe this (COB) should go in the second blank.

__

Then the line of interest would read ...

BOC + 30 + COB = 90

_____

<em>Comment on the problem</em>

There is a curious mix of notations here. Usually, (as in the beginning of this problem) we refer to the measure of an angle using "m∠" in front of the angle designator, and we use a degree symbol to indicate the units of that measure. Part-way through the problem statement written here, those notations were dropped, and we're to assume they are intended. IMO, this is a poor way to demonstrate careful problem solving.

The substitution given for AOC is BOC+30, but the line into which that is substituted has AOC +COB = 90. This means the equation after substitution is ...

BOC +30 +COB = 90

Since BOC and COB are the same angle, we can sort of fudge the "algebra" to get to BOC=30, but if the problem were more carefully written, the angle would be referred to by consistent nomenclature:

m∠AOC + m∠BOC = 90° . . . . . . . . . preferred angle designations

(m∠BOC + 30°) + m∠BOC = 90° . . . . substitution for m∠AOC

2(m∠BOC) = 60° . . . . . . algebra (subtract 30°, collect terms)

m∠BOC = 30° . . . . . . . . algebra (divide by 2)

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3 years ago