Question

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segment BD and EG are intersected by AH. Points of intersection are C and F. angle BCA is 1-6x. angle GFH is 2x+17.

Find the students error and show work to fix it.

The students work:

1-6x=2x+17
-1 -1
6x=2x+16
-2x -2x
4x=16
divide
- -
4 4
x=4

mGFH= 2x+17
= 2(4)+ 17
= 8+17
=25

Answer 1

The error is an algebraic sign mistake when they subtracted 1 from both sides.

Start with the given equation (assuming the two angles are congruent):
1 − 6x = 2x + 17

Correct steps:
1) Subtract 1 from both sides:
−6x = 2x + 16

2) Subtract 2x from both sides:
−8x = 16

3) Divide by −8:
x = 16 / (−8) = −2

Now find the angle measure:
m∠GFH = 2x + 17 = 2(−2) + 17 = −4 + 17 = 13°

(As a check, m∠BCA = 1 − 6x = 1 − 6(−2) = 1 + 12 = 13°, so the two angles match.)

The student’s mistake was at the first subtraction step: 1 − 6x − 1 should give −6x, not +6x. This led to the wrong x and wrong angle measure (they got x = 4 and m∠GFH = 25°). The correct answer is x = −2 and m∠GFH = 13°.