Solving Equations with Angle Measures 2--Example 5

Topic

Equations

Description

This example illustrates solving an equation involving angle measures in a rectangle. The rectangle has three known right angles (90°) and one unknown angle represented as (x+2x)°. To solve this problem, we use the property that the sum of angles in a rectangle is always 360°. We can set up the equation: (x+2x)° + 90° + 90° + 90° = 360°. Simplifying, we get 3x° + 270° = 360°. Subtracting 270° from both sides yields 3x° = 90°. Dividing by 3, we find x° = 30°. Therefore, the unknown angle (x+2x)° = 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. Such problems are essential in developing critical thinking skills and helping students understand the connection between algebra and geometry. They also prepare students for more complex problems involving quadrilaterals and angle relationships in advanced geometry courses.

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