Angle Addition Postulate - Varsity Tutors

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Angle Addition Postulate

Study Guide

Key Definition

The Angle Addition Postulate states that if you place an interior point on an angle and draw rays from that point to the sides, the sum of the two newly formed angles equals the measure of the original angle.

Important Notes

  • Angles are measured in degrees
  • If point D lies in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC
  • Angles that are next to each other and share a vertex are called adjacent angles
  • The angle addition postulate can be used to solve geometry problems involving angles

Mathematical Notation

$\angle ABC$ denotes the angle with vertex at B formed by rays BA and BC (points A and C on its sides).$m\angle ABC = 30°$ denotes the measure of ∠ABC in degrees.Remember to use proper notation when solving problems

Why It Works

Suppose point D is in the interior of ∠ABC, so rays BA, BD, and BC form two adjacent angles, ∠ABD and ∠DBC. By the definition of angle measure, m∠ABD + m∠DBC = m∠ABC, which is exactly the Angle Addition Postulate.

Remember

Always add up all the sub-angles to find the measure of the whole angle.

Quick Reference

Angle Addition Postulate:The sum of two angles formed by adding a point to an angle equals the measure of the original angle.

Understanding Angle Addition Postulate

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Video explanation of this concept

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Beginner Explanation

If point D is in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC.Now showing Beginner level explanation.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice QuizBeginner

If $\angle ACB$ is 60° and $\angle BCD$ is 30°, what is the measure of $\angle ACD$?

A$30°$B$60°$C$90°$D$120°$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.2

Real-World Problem

Question ExerciseIntermediate

Ice Cream Cone Scenario

An ice cream cone forms a 60° angle at the tip. A scoop of ice cream divides this into two angles of 30° and 30°. Is this possible? Explain your reasoning.Show AnswerClick to reveal the detailed solution for this question exercise.3

Thinking Challenge

Thinking ExerciseIntermediate

Think About This

If $\angle ACB$ is 50° and $\angle BCD$ is 70°, what is the measure of $\angle ACD$?

Show AnswerClick to reveal the detailed explanation for this thinking exercise.4

Challenge Quiz

Single Choice QuizAdvanced

If $\angle ACB$ is x and $\angle BCD$ is y, which of the following represents $\angle ACD$?

A$x - y$B$x + y$C$x * y$D$x / y$Check AnswerPlease select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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Review key concepts and takeaways

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