We will have the following:
First, we remember that suplementary angles add to 180°; knowing this, we can see that the supplementary angle for
We also remember that the sum of internal angles of a triangle also add to 180°, so the following is true:
[tex]m<\text{ACB}+m<\text{CAB}+m<\text{ABC}=180[/tex]
So:
[tex](3x)+(2x+40)+(180-(7x+10))=180\Rightarrow(3x)+(2x+40)+(170-7x)=180[/tex]
Now, we solve for x, that is:
[tex]\Rightarrow(3x)+(2x+40)+(170-7x)=180\Rightarrow-2x+210=180[/tex][tex]\Rightarrow-2x=-30\Rightarrow x=15[/tex]
Now, knowing this we will find the measure of angle ABC, that is:
[tex]m<\text{ABC}=170-7x\Rightarrow mSo,
the measure of the angle ABC is 65°.
