Question

Hi I’m major need of some help with this problem

Answer 1

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:

`m<\text{ACB}+m<\text{CAB}+m<\text{ABC}=180`

So:

`(3x)+(2x+40)+(180-(7x+10))=180\Rightarrow(3x)+(2x+40)+(170-7x)=180`

Now, we solve for x, that is:

`\Rightarrow(3x)+(2x+40)+(170-7x)=180\Rightarrow-2x+210=180`
`\Rightarrow-2x=-30\Rightarrow x=15`

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°.