Question

How do you prove angles are supplementary?

Answer 1

You must prove that the sum of both angles is equal to 180 degrees. ("If two angles form a linear pair, then they are supplementary; that is, the sum of their measures is 180 degrees.")

Explanation:

A good way to start is to look at your geometric theorems and think about if you could use any to determine the measurement of your angles.

A few ways to consider include:

a) Determine the measurement of `/_` `ABC` and the measurement of `/_` `ABD`, and prove that the combined measurements`=180` degrees.

b) Determine that the measurement of `/_CBD=180` degrees. If you choose this method, you can use the linear pairs postulate to prove that since the measure of `/_CBD=180` degrees, the angles that are added to form this angle (`/_ABC` and `/_ABD`) must be supplementary.

You can find a comprehensive list of geometric theorems here:
http://www.rio.k12.wi.us/M_Hschool/math/geo1.html

This is also the source from which I retrieved the theorem I posted in the above answer.