supplemntary angle , help

[drgzn471125]

< ABC and < CBD are supplementary. If m< ABC = (7x+13) and m< CBD = (3x+7), what is m< ABC?

I got an of 16 degrees, which is wrong, but the answer is 125 degrees. I just dont see how this answer came about. Need some explanation on how to arrive with 125 degrees as the correct answer.

 

[soroban]

Hello, drgzn471125!

Your work is correct . . . But you didn't answer the question.

\(\displaystyle \angle ABC\text{ and }\angle CBD\text{ are supplementary.}\)

\(\displaystyle \text{If }\angle ABC \:= \:7x+13\text{ and }\angle CBD \:= \:3x+7}\text{, find }\angle ABC.\)

\(\displaystyle \text{I assume you had: }\;(7x + 13) + (3x + 7) \:=\:180\)
. . \(\displaystyle \text{And solved for }x\!:\;\;x\:=\:16\)

\(\displaystyle \text{Now what was the question? . . . Find }\angle ABC.\)


\(\displaystyle \text{We are told that: }\;\angle ABC \:=\:7x+13\)

\(\displaystyle \text{Therefore: }\;\angle ABC \:=\;7(16) + 13 \:=\:125^o\)

. . . . There!

 

[nycfunction]

< ABC and < CBD are supplementary. If m< ABC = (7x+13) and m< CBD = (3x+7), what is m< ABC?

I got an of 16 degrees, which is wrong, but the answer is 125 degrees. I just dont see how this answer came about. Need some explanation on how to arrive with 125 degrees as the correct answer.

I think we need to define supplementary angle. What is a supplementary angle? Angles are supplementary if their measurements add up to 180 degrees. You were given two angles: angle ABC and angle CBD.

(1) Add and equate both angles to 180 degrees.

angle ABC + angle CBD = 180 degrees

7x + 13 + 3x + 7 = 180 degrees

Next: Solve for x.

10x + 20 = 180

10x = 180 - 20

10x = 160

x = 160 divided by 10

x = 16

We found the right value for x but your question is asking for the measure of angle ABC, which is (7x + 13).

(2) We now need to replace x in the quantity (7x + 13) with 16 and simplify to find the measure of angle ABC.

angle ABC = (7x + 13) = 7(16) + 13 = 112 + 13 = 125 degrees

So, angle ABC = 125 degrees

 

[drgzn471125]

Yes!! Thank you both....for your answer and to show me I needed tone more step to finish....