Solving Equations with Angle Measures--Example 8

Topic

Equations

Description

This example demonstrates solving an equation involving angle measures in a right triangle where the two acute angles are expressed in terms of a variable. The triangle has a right angle (90°) and two unknown angles represented as 2x° and 3x°. To solve this problem, we apply two principles: the sum of angles in a triangle is 180°, and in a right triangle, the two acute angles are complementary (sum to 90°). We can set up the equation: 90° + 2x° + 3x° = 180°. Alternatively, we could use 2x° + 3x° = 90°. Using the first equation and simplifying, we get 5x° = 90°. Dividing by 5, we find x° = 18°. Therefore, the two acute angles are 2x° = 36° and 3x° = 54°. This problem reinforces the properties of right triangles and introduces algebraic representation of angles. It challenges students to apply their knowledge of triangle properties while manipulating algebraic expressions. Such problems are crucial in developing analytical thinking and preparing students for more advanced concepts in geometry and trigonometry. They also help students understand the relationship between different angles in a right triangle and how they can be represented algebraically.

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