The main idea behind the Angle Addition Postulate is that if you place two angles side-by-side then the measure of the resulting angle will be equal to the sum of the two original angle measures. For this postulate to apply, the vertices, which are the corner points of the angle, have to also be placed together. We can illustrate this idea by using the heads of two arrows. We are going to label the arrowheads with some points to make it easier to name the angles.

Angle Addition Postulate states that if a point S lies in the interior of ∠PQR, then ∠PQS + ∠SQR = ∠PQR.

If the sum of the two angles measure up to 900, then the angles are called to be ‘complementary angles’.

If the sum of the two angles measure up to 1800, then the angles are called to be ‘supplementary angles’.

The angles sharing a common side are called as ‘adjacent angles’.

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