In triangle ABC, line segment BC is extended through point C to point D. If m(angle)A=43 and m(angle)BCD=123, then m(angle)ABC=
1.)62
2.)80
3.)14
4.)166

Question

In triangle ABC, line segment BC is extended through point C to point D. If m(angle)A=43 and m(angle)BCD=123, then m(angle)ABC=
1.)62
2.)80
3.)14
4.)166

mathstudent55 · Answer

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If line segment BC is extended to point D, m<BCD = 180. How can it be 123?

mathstudent55 · Answer

Is the angle that measures 123 BCD or ACD?

anonymous · Answer

Angle BCD=123

mathstudent55 · Answer

Is the side that is extended BC or AC? In other words, did you copy the problem correctly?

anonymous · Answer

yes

mathstudent55 · Answer

Then this problem is incorrect. I think they want to make the angle that measures BCD an exterior angle. The measure of an exterior angle equals the sum of the measures of the remote interior angles. I think the intent of the problem may be to use the above fact about an exterior angle of a triangle. In this case this would be m<A + m<ABC = 123, and since m<A = 43, that makes m<ABC = 80. But there is an error with this problem as it is stated.

anonymous · Answer

This is the problem: In triangle ABC, line segment BC is extended through point C to point D. If m(angle)A=43 and m(angle)=123, then m(angle)ABC=

anonymous · Answer

the bc looks lilke this in thr problem" -
                                                      BC

mathstudent55 · Answer

BC with a bar on top? That just means line segment BC.

anonymous · Answer

yeah i know I dont get any of this!

mathstudent55 · Answer

Wait, when you retyped the problem you left something out. Look a tthe last line: "If m(angle)A=43 and m(angle)=123, then m(angle)ABC=" 
What is m(angle)=123. Which angle has measure 123?

anonymous · Answer

angle BCD is 123

anonymous · Answer

angle A=43

mathstudent55 · Answer

Right. That's the same you had originally. I still say there is an error in this problem.

mathstudent55 · Answer

I think they meant m<ACD = 123. The m<BCD has to be 180, and that is only if Geometry allows for a 180-degree angle.

anonymous · Answer

okay so whats my answer?

mathstudent55 · Answer

As the problem is stated there is no answer. If it's m<ACD = 123 instead of m<BCD = 123, then this is what you do:
m<A + m<ABC = m<ACD
43 + m<ABC = 123
m<ABC = 123 - 43
m<ABC = 80

anonymous · Answer

<BCD=123 and <A=43... I need to find m<ABC

mathstudent55 · Answer

Didn't I just do that just above? Of course, that is for the problem the way I modified it. The problem, as you wrote it, has no solution bec there is an error in it.

anonymous · Answer

okay thanks(:

mathstudent55 · Answer

You're welcome.
If you have a teacher for this, try to clear up this problem.