Solving Equations with Angle Measures--Example 15

Topic

Equations

Description

This example demonstrates solving equations involving angle measures in a triangle using the properties of supplementary angles. The triangle has one known angle of 50° and two unknown angles represented by x° and y°. We're also informed that the angle supplementary to y° is 90°. To solve this problem, we apply two key principles: the sum of angles in a triangle is 180°, and supplementary angles sum to 180°. We start by calculating y°: since 50° + y° = 90° (supplementary angles), y° = 40°. Now we can set up the equation for the triangle: 50° + x° + 40° = 180°. Solving for x°, we get x° = 90°. This problem is particularly noteworthy because it results in a right angle (90°) within the triangle, making it a right triangle. It showcases how supplementary angle relationships can lead to the discovery of special triangle types. This example helps students understand the connection between supplementary angles and right triangles, a crucial concept in geometry and trigonometry. Such problems enhance students' ability to visualize and analyze complex geometric relationships, preparing them for more advanced mathematical concepts and real-world applications in fields like engineering and architecture.

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