Solving Equations with Angle Measures--Example 10

Topic

Equations

Description

This example demonstrates solving an equation involving angle measures in an isosceles triangle. The triangle has two equal angles represented by x° and a known angle of 50°. To solve this problem, we apply two key principles: the sum of angles in a triangle is 180°, and an isosceles triangle has two equal angles. We can set up the equation: x° + x° + 50° = 180°. Simplifying, we get 2x° + 50° = 180°. Subtracting 50° from both sides yields 2x° = 130°. Dividing by 2, we find x° = 65°. This problem showcases the unique properties of isosceles triangles and how they can be used in angle calculations. It reinforces the concept that the two equal angles in an isosceles triangle are always opposite the two equal sides. Such problems are crucial in developing a deeper understanding of triangle properties and their application in geometry. They help students recognize patterns in geometric figures and translate these patterns into algebraic equations. This example also serves as a foundation for more complex problems involving isosceles triangles, preparing students for advanced topics in geometry and trigonometry.

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