Solving Equations with Angle Measures--Example 13

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 55° and two unknown angles represented by x° and y°. We're also given that the angle supplementary to y° is 130°. To solve this problem, we apply two key principles: the sum of angles in a triangle is 180°, and supplementary angles sum to 180°. First, we can find y° using the supplementary angle information: y° + 130° = 180°, so y° = 50°. Now we can set up the equation for the triangle: 55° + x° + 50° = 180°. Solving for x°, we get x° = 75°. This problem showcases how to use supplementary angle relationships in conjunction with triangle properties to solve for unknown angles. It requires students to apply multiple geometric concepts simultaneously, enhancing their problem-solving skills. Such problems are crucial in developing a deeper understanding of angle relationships in various geometric configurations, preparing students for more complex scenarios in advanced geometry and trigonometry.

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