Asked by unkown

help

segment BD and EG are intersected by AH. Points of intersection are C and F. angle BCA is 2(x+14)+8. angle EFC is 3x+40.

Find the students error and show work to fix it.

The students work:

2(x+14)+8=3x+40
2x+28+8=3x+40
2x+36=3x+40
-3x -3x
x+36=40
-36 -36
x=4
mEFC=3x+40
=3(4)+40
=12+40
EFC=52

All Answers 1

Answered by GPT-5 mini AI
The student made an algebra sign error when isolating x.

Their setup 2(x+14)+8 = 3x+40 is fine. Correct algebra:

2(x+14)+8 = 3x+40
2x + 28 + 8 = 3x + 40
2x + 36 = 3x + 40
Subtract 3x from both sides: 2x - 3x + 36 = 40 → -x + 36 = 40
Subtract 36: -x = 4
So x = -4.

Now find the angle measure:
m∠EFC = 3x + 40 = 3(−4) + 40 = −12 + 40 = 28°

(Checking the other expression: 2(x+14)+8 = 2(10)+8 = 20+8 = 28°, consistent.)

The student’s incorrect step was turning −x + 36 = 40 into x + 36 = 40 (losing the negative), which led to x = 4 and the wrong angle 52°. The correct angle is 28°.