Angle Addition Postulate

If m∠ABX + m∠XBC is less than or equal to 180, then m∠ABX + m∠XBC is m∠ABC.

What if m∠ABX + m∠XBC was greater than 180? Take a look at an example:

A C B X 90° 135° 135°

m∠ABX is 135° and m∠XBC is 135°. Thus, m∠ABX + m∠XBC = 270°. However, m∠ABC is 90° rather than 270°. This is because a measurement of the angle is always the smallest rotation from one ray of the angle to the other (see angle).

if ((m∠ABX) + (m∠XBC) < 180) or ((m∠ABX) + (m∠XBC) = 180), then m∠ABC = (m∠ABX) + (m∠XBC)
A C B X

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