Solving Equations with Angle Measures--Example 14

Topic

Equations

Description

This example illustrates solving equations involving angle measures in a triangle using the properties of supplementary angles. The triangle has one known angle of 35° and two unknown angles represented by x° and y°. We're also given that the angle supplementary to y° is 50°. To solve this problem, we apply two fundamental principles: the sum of angles in a triangle is 180°, and supplementary angles sum to 180°. We begin by determining y°: y° + 50° = 180°, so y° = 130°. Now we can set up the equation for the triangle: 35° + x° + 130° = 180°. Solving for x°, we find x° = 15°. This problem is particularly interesting because it results in a very obtuse angle (130°) within the triangle, which is unusual in typical triangle problems. It challenges students to think beyond conventional triangle shapes and reinforces the idea that the sum of angles in a triangle is always 180°, regardless of the individual angle measures. Such problems are essential in developing critical thinking skills and a deeper understanding of geometric principles, preparing students for more advanced concepts in mathematics.

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