Question

help

segment BD and EG are intersected by AH. Points of intersection are C and F. angle ACD is 4x-2(x+6). angle GFC is 5x+13-4x.

Find the students error and show work to fix it.

The students work:

4x-2(x+6)=5x+13-4x
4x+2x-12=x+13
6x-12=x+13
-x -x
5x-12=13
+12 +12
5x-25
divide
- -
5 5
x= 5

mCFG= 5(5)+13-4(5)
=25+13-20
=18

Answer 1

The student made a sign/distribution error when simplifying 4x − 2(x + 6).

Start from the equation (given by corresponding/alternate angles)
4x − 2(x + 6) = 5x + 13 − 4x.

Correct simplification:
4x − 2(x + 6) = 4x − 2x − 12 = 2x − 12.
Right side: 5x + 13 − 4x = x + 13.

So the equation is
2x − 12 = x + 13.

Solve:
2x − x = 13 + 12
x = 25.

Now find the angle measure. Using either expression (they are equal), for example 5x + 13 − 4x = x + 13:
m∠GFC = x + 13 = 25 + 13 = 38°.

(Check with the other expression: 4x − 2(x + 6) = 4(25) − 2(31) = 100 − 62 = 38°.)

So the student’s error was the wrong sign when distributing −2 (they wrote +2x instead of −2x). The correct answer is x = 25 and the angle measure is 38°.