In triangle ABC , AC is extended through C to D .
if m

Question

In triangle ABC , AC is extended through C to D . 
if m<BCD=2X+35 , m<BAC=x-3 and m<ABC=3x-20 
what is the value of x?

1) 28
2) 30
3) 29
4) 31

mathstudent55 · Answer

This is what you have

|dw:1388619994859:dw|

anonymous · Answer

It would be 28

anonymous · Answer

We can add all the equations and equal it to 180

mathstudent55 · Answer

Sorry, but the above explanation and solution are incorrect. x≠28.

Notice that the angle measuring 2x + 35 is not an interior angle, so the sum of its measure and the measures of the other two interior angles is not necessarily 180. 

You need this theorem:
In a triangle, the measure of any exterior angle equals the sum of the measures of its two remote interior angles. 

That means: 

3x - 20 + x - 3 = 2x + 35

4x - 23 = 2x + 35

2x = 58 

x = 29

anonymous · Answer

That is correct!! I ignored it. Thanks

mathstudent55 · Answer

There is a way of solving this problem by adding the measures of the 3 interior angles and setting the sum equal to 180. First, though, you need to find the measure of the third angle. See the figure below.

|dw:1388621324989:dw|

Now we have the three interior measures.

3x - 20 + x - 3 + 180 - (2x + 35) = 180

3x - 20 + x - 3 + 180 - 2x - 35 = 180

2x + 122 = 180

2x = 58

x = 29