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A Look at the Angle Addition Postulate

The angle addition postulate is a theorem in geometry that states that the measure of an angle formed by two adjacent angles is the sum of the measures of the two angles. In other words, if you have two angles side-by-side, the total measure of those two angles combined is equal to the sum of each angle individually.


Let’s take a closer look at this theorem and how it can be applied in the real world.


How It Works

The angle addition postulate states that the measure of Angle BAC is equal to the sum of Angle ABD and Angle DBC. This theorem can be represented using the following equation: m<sup>∠</sup>BAC=m<sup>∠</sup>ABD+m<sup>∠</sup>DBC.


This theorem can be applied in a variety of scenarios, such as measuring the length of an unknown side in a triangle or solving for an interior angle in a polygon.


A Real-World Example

Let’s say you’re trying to find the measure of Angle ABC in the triangle shown below.


Triangle ABC has two known sides, AC and BC. However, the measure of Angle ABC is unknown. To solve for this angle, we can use the angle addition postulate. We already know that m<sup>∠</sup>A=37° and m<sup>∠</sup>C=53°, so we can plug those values into our equation. We also know that m<sup>∠</sup>BAC=m<sup>∠</sup>ABD+m<sup>∠</sup>DBC, so we can solve for m<sup>∠</sup>BAC by adding 37°+53°=90°. This tells us that m<sup>∠</sup>ABC=90°.


The angle addition postulate is a simple yet powerful theorem that can be used to solve a variety of problems in geometry. Next time you’re struggling to find the measure of an angle or side in a geometric figure, remember this theorem and put it to good use!

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