Question

I beg help me finish this HW

Answer 1

Answer: The mixed number 16 1/3

Some books write this as 16 & 1/3 to help separate out the whole part (16) and the fractional part (1/3) better.

On paper, you'd write it as $16 \frac{1}{3}$

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Explanation:

The three angles mentioned (AOC, DOC, EOD) all combine to form a straight angle AOD = 180 degrees

So we can say,

(angle AOC) + (angle DOC) + (angle EOD) = angle AOD

(angle AOC) + (angle DOC) + (angle EOD) = 180

(7x-2) + (2x+8) + (27) = 180

7x-2 + 2x+8 + 27 = 180

(7x+2x) + (-2+8+27) = 180

9x+33 = 180

9x = 180-33 ... subtract 33 from both sides

9x = 147

x = 147/9 .... divide both sides by 9

x = 16.333333 .... use calculator here

The stuff to the left of the decimal (16) is the whole part

The decimal part 0.33333 where the 3's go on forever converts to 1/3

We can see this if we multiply 0.33333 with 9 getting 0.33333*9 = 2.99997

and that rounds to 3, so 3/9 = 1/3

In short, 16.333333 = 16 & 1/3