Answer:
[tex]\huge\boxed{B}[/tex]
Explanation:
Hi there!
A) [tex]m\angle1 + m\angle3 = m\angle6\\[/tex]
B) [tex]m\angle1+m\angle3=m\angle2[/tex]
C) [tex]m\angle2+m\angle3=m\angle5[/tex]
D) [tex]m\angle1 + m\angle2 = m\angle4[/tex]
Let's start with a
How would [tex]m\angle1 + m\angle3 = m\angle6\\[/tex] ?
Well, [tex]m\angle1[/tex] and [tex]m\angle3[/tex] are inside the triangle, and [tex]m\angle6[/tex] is right across from it (see image provided with question), which means they are remote interior angles, meaning this statement is correct. A is not the answer.
How would [tex]m\angle1+m\angle3=m\angle2[/tex]?
There is no rule that 2 angles in a triangle have to add up to the other one, so this statement is incorrect. B is the answer. Let's make sure none of the others are incorrect as well.
How would [tex]m\angle2+m\angle3=m\angle5[/tex]?
Just like A, this is another case of remote interior angles, where [tex]m\angle2+m\angle3=m\angle5[/tex]. This option is correct due to this proof.
How would [tex]m\angle1+m\angle2=m\angle4[/tex]?
Another case of remote interior angles as you can see from the image, which means that this equation is correct.
The correct answer is B, as that is the only statement that is false.
[tex]\huge\boxed{B}[/tex]
Hope this helps :)
Let me know if you have any questions!
