Question

help

segment BD and EG are intersected by AH. Points of intersection are C and F. angle ACD is x+8+2x. angle EFH is 2(2x-5).

Find the students error and show work to fix it.

The students work:

2(2x-5)+x+8+2x=180
4x-10+x+8+2x=180
7x-10+8=180
7x-2=180
+2 +2
7x=182
divide
- -
7 7
x=26

mEFH=2(2x-5)
=2[2(26)-5]
=2[52-5]
=2[47]
EFH=94

Answer 1

Summary of the student’s error
- The student assumed the two given angles were supplementary (added them and set their sum = 180). That assumption is incorrect.
- If BD and EG are parallel and AH is a transversal, angle ACD and angle EFH are corresponding (or congruent) angles, so they are equal, not supplementary.

Correct work
1. Write the angle measures in simpler form:
- angle ACD = x + 8 + 2x = 3x + 8
- angle EFH = 2(2x − 5) = 4x − 10

2. Because BD ∥ EG and AH is a transversal, corresponding angles are equal:
3x + 8 = 4x − 10

3. Solve for x:
3x + 8 = 4x − 10
8 + 10 = 4x − 3x
18 = x

4. Find the angle measures:
- angle EFH = 4x − 10 = 4(18) − 10 = 72 − 10 = 62°
- angle ACD = 3x + 8 = 3(18) + 8 = 54 + 8 = 62°

Conclusion
- The student’s algebra was performed correctly for the equation they set up, but the geometric relationship used (supplementary) was wrong. The correct relation is equality, so x = 18 and each angle measures 62°.