unit 1 geometry homework 4 angle addition postulate

Angle Addition Postulate

The angle addition postulate in geometry states that if we place two or more angles side by side such that they share a common vertex and a common arm between each pair of angles, then the sum of those angles will be equal to the total sum of the resulting angle. For example, if ∠AOB and ∠BOC are adjacent angles on a common vertex O sharing OB as the common arm, then according to the angle addition postulate, we have ∠AOB + ∠BOC = ∠AOC.

Angle Addition Postulate Definition

The definition of angle addition postulate states that "If a ray is drawn from point O to point P which lies in the interior region of ∠MON, then ∠MOP + ∠NOP = ∠MON". This postulate can be applied to any pair of adjacent angles in math. In other words, the angle addition postulate can be defined as 'the sum of two angles joined together through a common arm and a common vertex is equal to the sum of the resulting angle formed'.

Angle Addition Postulate Formula

If an angle AOC is given where O is the vertex joining rays OA and OC, and there lies a point B in the interior of ∠AOC, then the angle addition postulate formula is given as ∠AOB+∠BOC = ∠AOC. If ∠AOC is divided into more than two angles such as ∠AOB, ∠BOD, and ∠DOC, then also we can apply the formula of angle addition postulate as ∠AOB+∠BOD+∠DOC = ∠AOC.

Topics Related to Angle Addition Postulate:

Check these interesting articles related to the concept of angle addition postulate in math.

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Angle Addition Postulate Examples

Example 1: In the figure given below, if ∠POS is a right angle, ∠2 = 30°, and ∠3 = 40°. Find the value of ∠1.

Solution: It is given that ∠POS is a right angle. It means that ∠POS = 90°. Now, by using the angle addition postulate formula, we can write ∠1 + ∠2 + ∠3 = 90°. Given, ∠2 = 30° and ∠3 = 40°. Substituting these values in the above equation, we get,

∠1 + 30° + 40° = 90°

∠1 + 70° = 90°

∠1 = 90° - 70°

Therefore, the value of ∠1 is 20°.

Example 2: In the given figure, XYZ is a straight line. Find the value of x using the angle addition postulate.

Solution: It is given that XYZ is a straight line. It means that ∠XYO and ∠OYZ form a linear pair of angles.

⇒ ∠XYO + ∠OYZ = 180° (using angle addition postulate and linear pair of angles property)

⇒ (3x + 5) + (2x - 5) = 180°

⇒ 5x = 180°

Therefore, the value of x is 36.

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Practice Questions on Angle Addition Postulate

Faqs on angle addition postulate, what is angle addition postulate in geometry.

The angle addition postulate in geometry is a mathematical axiom which states that if there is a ray drawn from O to Q which is any point inside the region of angle POR, then the sum of angles ∠POQ and ∠QOR is equal to ∠POR. It can be represented in the form of a mathematical equation as ∠POQ + ∠QOR = ∠POR.

What is the Angle Addition Postulate Formula?

The formula of angle addition postulate in math is used to express the sum of two adjacent angles. If there are two angles (∠AOB and ∠BOC) joined together sharing a common arm OB and a common vertex O, then the angle addition postulate formula is ∠AOB + ∠BOC = ∠AOC.

How to Find x in Angle Addition Postulate?

If there is any missing angle 'x' when two or more angles are joined together, then we can subtract the sum of remaining angles from the total sum to find the value of x. For example, if two angles ∠PQR and ∠RQS are joined together such that ∠RQS = 40°, ∠PQR = x, and ∠PQS = 70°, then the value of x will be (70 - 40)° = 30°.

How to Use Angle Addition Postulate?

The angle addition postulate can be used to find the sum of two or more adjacent angles and to find the missing values of angles. It establishes a relation between the measurement of angles joined together.

How do you Find the Angle Addition Postulate?

The angle addition postulate is a mathematical fact that can be considered true without any proof. It tells us that the sum of two or more angles joined together is equal to the sum of the larger angle formed.

How is the Angle Addition Postulate Used in Real Life?

In real life, the angle addition postulate is used in construction (bridges, buildings, etc), architecture, designing, etc.