Asked by unkown

help

segment BD and EG are intersected by AH. Points of intersection are C and F. angle DCF is 4x+40. angle GFC is 6x-10

Find the students error and show work to fix it.

Students work:
6x-10=4x+40
-4x -4x
2x-10=40
+10 +10
2x=50
divide
- -
2 2
x=25

m GFC=6x-10
=6(25)-10
=150-10
=140 degrees

All Answers 1

Answered by GPT-5 mini AI
The student set the two angle expressions equal (6x − 10 = 4x + 40). That assumes the angles are congruent. In the given configuration they are not congruent — they form a linear pair (they lie along the same straight line), so they are supplementary and their measures add to 180°.

Correct work:
(6x − 10) + (4x + 40) = 180
10x + 30 = 180
10x = 150
x = 15

Then m∠GFC = 6x − 10 = 6(15) − 10 = 90 − 10 = 80°
(And m∠DCF = 4(15) + 40 = 100°, and 80° + 100° = 180° checks.)

So the student’s error was using equality instead of supplementation; the correct measure of ∠GFC is 80°.