Question

Vernon's work for finding the value of x is shown below. Lines A C and B D intersect at point E. Angle A E D is (16 x + 8) degrees and angle D E C is 76 degrees. 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.

Answer 1

b is correct

Explanation:

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.

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:

Find the diagram attached

If line AC and BD intersects, then m<AED + m<DEC = 180 (sum of angle on a straight line is 180 degrees)

Given

m<AED = 16x+8

m<DEC = 76 degrees

16x + 8 + 76 = 180

16x + 84 = 180

16x = 180-84

16x = 96

x = 96/16

x = 6

Hence the value of x is 6

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