Equations Using the Exterior Angle Theorem--Example 8

Topic

Equations

Description

This example showcases another application of the Exterior Angle Theorem in solving triangle-related equations. In this scenario, we have a triangle with an unknown interior angle y, a known interior angle of 25°, and a known exterior angle of 92°. 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 92° = y + 25°. This problem demonstrates how the theorem can be used to find an unknown interior angle when given one interior angle and the exterior angle. To solve for y, we subtract 25° from both sides, resulting in y = 67°. By finding y, you can then solve for x using the triangle equation.

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 reinforces both geometric understanding and algebraic skills. By working through this type of problem, students enhance their ability to apply theoretical concepts to practical geometric situations. This example serves as an excellent exercise in critical thinking and problem-solving, preparing students for more complex mathematical challenges in geometry and beyond.

For a complete collection of math examples related to Equations That Use the Exterior Angle Theorem click on this link: Math Examples: Equations That Use the Exterior Angle Theorem Collection.