Question

Vernon’s work for finding the value of x is shown below.


Step 1: 16x + 8 = 76
Step 2: 16x = 68
Step 3: x = 4.25

Did Vernon solve for the correct value of x? If not, explain where he made his error.

Yes, he solved for the correct answer.

No, he should have set the sum of ∠AED and ∠DEC equal to 180°, rather then setting ∠AED and ∠DEC equal to each other.

No, he should have added 8 to both sides rather than subtracting 8 from both sides.

No, he should have multiplied both sides by 16 rather than dividing both sides by 16.


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Answer 1

B is the answer.

Explanation:

Yes, he solved for the correct answer.

No, he should have set the sum of ∠AED and ∠DEC equal to 180°, rather than setting ∠AED and ∠DEC equal to each other.

No, he should have added 8 to both sides rather than subtracting 8 from both sides.

No, he should have multiplied both sides by 16 rather than dividing both sides by 16.

Answer 2

No, he should have set the sum of ∠AED and ∠DEC equal to 180°, rather then setting ∠AED and ∠DEC equal to each other.

Explanation:

He was using the measurements of m∠AED & m∠CED, which are supplementary angles, not vertical angles (therefore making them, when combined, equal to 180°).

If they were vertical angles (at the case of m∠AED & m∠BEC, or the other pair), then yes, they will be congruent. But in this case, they are not, so you don't solve it like they are vertical angles.

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