Solving Equations with Angle Measures--Example 2

Topic

Equations

Description

This example illustrates solving an equation involving angle measures in a triangle where two angles are expressed in terms of a variable. The triangle has one known angle of 60° and two unknown angles represented as x° and 2x°. To solve this problem, we apply the principle that the sum of angles in a triangle is 180°. We can set up the equation: 60° + x° + 2x° = 180°. Simplifying, we get 60° + 3x° = 180°. Subtracting 60° from both sides yields 3x° = 120°. Dividing by 3, we find x° = 40°. Consequently, the third angle (2x°) is 80°. This problem introduces a more complex scenario compared to the previous example, as it involves multiple unknown angles expressed in terms of a single variable. It requires students to apply both their knowledge of triangle properties and algebraic skills. Such problems are essential in developing critical thinking and problem-solving abilities in geometry. They prepare students for more advanced concepts by teaching them how to handle equations with multiple variables and terms, a crucial skill in higher-level mathematics.

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