Question

Solve for $x$ in each of these figures. (GRAPH CANT COPY)

   Solve for $x$ in each of these figures.
(GRAPH CANT COPY)

Geometry

Harold R. Jacobs 2nd Edition

Chapter 8, Problem 13

Instant Answer

Solved by Expert Christopher Stanley

07/31/2020

Step 1

In the first figure, we have a triangle with angles 30°, 60°, and 90°. The side opposite the 30° angle is labeled as x, and the side opposite the 60° angle is labeled as 2x. Since this is a 30-60-90 triangle, we know that the ratio of the sides is 1:√3:2. Show more…

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Solve for $x$ in each of these figures. (GRAPH CANT COPY)

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Key Concepts

Algebraic Manipulation

This concept involves using basic operations (addition, subtraction, multiplication, and division) to isolate the unknown variable, x, on one side of the equation. It includes combining like terms, using inverse operations, and maintaining the balance of the equation throughout the process. Mastery of algebraic manipulation is crucial for solving any algebra-based equation or problem derived from a diagram or figure.

Geometric Reasoning

When solving for x in figures, understanding the inherent geometric relationships is key. This includes knowing properties such as congruent and supplementary angles, properties of parallel lines, triangles, and other polygons, as well as recognizing similar shapes and proportional relationships. These geometric properties allow one to translate visual information into algebraic equations that can then be solved using algebraic manipulation.

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