Asked by unkown

can you help me i think i know the answer but i'm stuck

Fred solves the following problem incorrectly. Find and explain where he went wrong and then solve the problem correctly yourself. Show ALL work on paper (handwritten work) to receive credit.

Ray BD lies in the interior of ∠ABC. If m∠ABD=3x+10° and m∠DBC=2x+25° and m∠ABC=95°
find the value of x and the measure of each angle.

Fred's work to solve for x:

m∠ABD+m∠DBC=m∠ABC

(3x+10)+(2x+25)=95

5x+15=95

5x=80

x=16

All Answers 1

Answered by GPT-5 mini AI
Fred’s setup is correct (the two smaller angles add to the larger one), but he made an arithmetic mistake when combining constants.

Where Fred went wrong:
- He wrote (3x + 10) + (2x + 25) = 95, which is correct.
- But (3x + 10) + (2x + 25) = 5x + 35, not 5x + 15. He added 10 + 25 incorrectly.

Correct solution (showing all algebra steps you should copy neatly by hand):

1. Use the fact that ray BD is interior to ∠ABC, so
m∠ABD + m∠DBC = m∠ABC.

2. Substitute the expressions:
(3x + 10) + (2x + 25) = 95.

3. Combine like terms:
3x + 2x + 10 + 25 = 95
5x + 35 = 95.

4. Solve for x:
5x = 95 − 35
5x = 60
x = 12.

5. Find each angle measure:
m∠ABD = 3x + 10 = 3(12) + 10 = 36 + 10 = 46°.
m∠DBC = 2x + 25 = 2(12) + 25 = 24 + 25 = 49°.
Check: 46° + 49° = 95°, which matches m∠ABC.

Answer: x = 12; m∠ABD = 46°, m∠DBC = 49°.