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`