Solving Equations with Angle Measures--Example 5

Topic

Equations

Description

This example showcases solving an equation involving angle measures in a triangle with one known angle and two related unknown angles. The triangle has a given angle of 110°, with the other two angles expressed as (x+10)° and x°. To solve this problem, we apply the principle that the sum of angles in a triangle is 180°. The equation can be set up as 110° + (x+10)° + x° = 180°. Simplifying, we get 110° + x° + 10° + x° = 180°, which reduces to 120° + 2x° = 180°. Subtracting 120° from both sides yields 2x° = 60°. Dividing both sides by 2, we find x° = 30°. Consequently, the second unknown angle is (x+10)° = 40°. This problem introduces a more complex scenario compared to the previous example, as it involves algebraic expressions for two of the angles. 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 and real-world applications.

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