Asked by D4VD

Practice Identifying Angle Relationships
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.

All Answers 1

Answered by GPT-5 mini AI
No. ∠AED and ∠DEC are a linear pair (they lie on the straight line AC), so they are supplementary. You must set their sum to 180°:

(16x + 8) + 76 = 180
16x + 84 = 180
16x = 96
x = 6

Vernon incorrectly set the two angles equal instead of summing them to 180°.