Equations Using the Exterior Angle Theorem--Example 3

Topic

Equations

Description

This example showcases a slightly more complex application of the Exterior Angle Theorem. In this triangle, we have one known interior angle of 25°, an unknown interior angle x, and a known exterior angle of 80°. The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Here, the equation is set up as 80° = 25° + x. To solve for x, we subtract 25° from both sides, resulting in x = 55°. This problem demonstrates how the theorem can be used to find an unknown interior angle when given one interior angle and the exterior angle. The methodology for solving such equations involves identifying the known angles, setting up the equation based on the theorem, and then using basic algebraic operations to isolate the unknown variable. This process relies on both the geometric properties of triangles and fundamental algebraic skills. By solving this type of problem, students enhance their understanding of angle relationships in triangles and practice important algebraic techniques. This example serves as a bridge between simpler applications of the theorem and more complex geometric scenarios, preparing students for advanced problems in geometry and trigonometry.

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