Solving Equations with Angle Measures 2--Example 6

Topic

Equations

Description

This example demonstrates solving an equation involving angle measures in a rectangle. The rectangle has three known right angles (90°) and one unknown angle represented as (x+x+15)°. To solve this problem, we apply the property that the sum of angles in a rectangle is always 360°. We can set up the equation: (x+x+15)° + 90° + 90° + 90° = 360°. Simplifying, we get 2x° + 15° + 270° = 360°. Combining like terms, we have 2x° + 285° = 360°. Subtracting 285° from both sides yields 2x° = 75°. Dividing by 2, we find x° = 37.5°. Therefore, the unknown angle (x+x+15)° = 90°, confirming that all angles in the rectangle are indeed 90°. This problem reinforces the fundamental property of rectangles having four right angles. It demonstrates how algebraic equations can be used to verify geometric properties, even when the unknown angle is expressed as a more complex algebraic expression. Such problems are crucial in developing students' ability to translate between geometric concepts and algebraic representations, preparing them for more advanced topics in mathematics.

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