Question

2. Two angles have a common vertex but no common side. How can you tell whether the angles are vertical angles?

Answer 1

Explanation:

The angles are vertical angles if the opposites of the rays forming one of the angles are the rays forming the other angle.

More formally, if V is the common vertex, and ...

• R is a point on one of the rays forming Angle 1
• S is a point on the ray that is the opposite of ray VR
• T is a point on the other ray forming Angle 1
• U is a point on the ray that is the opposite of ray VT

Then angle RVT and angle SVU are vertical angles.

___

Another way to say this is that points R, V, S are collinear, as are points T, V, U, and the two angles of interest are RVT and SVU.

If the above conditions cannot be met, then the angles are not vertical angles.