Question

Given: <2 and <4 are vertical angles.Prove: <2 = <4

Answer 1

We can see that

$\angle2+\angle3\text{ =180\degree}$

since they are on a straight line. Likewise,

$\angle3+\angle4=180\degree$

We now have the equation

$\angle2+\angle3=\angle3+\angle4$

Substracting from both sides of the equation we get

$\angle2+\angle3-\angle3=\angle3+\angle4-\angle3$

And thus

$\angle2=\angle4$