Solving Equations Using Triangle Properties: Example 4

Topic

Equations

Description

This example demonstrates solving equations using the Exterior Angle Theorem in the context of parallel lines cut by a transversal, two crucial concepts in geometry. The problem presents a triangle with two known interior angles of 80° and y, and an unknown exterior angle x°. 

We are also given that 80 - y = 50, which simplifies to y = 30. The goal is to determine the value of x using the properties of triangles and the Exterior Angle Theorem. The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Wo we get x = 80 + 30, or x = 110.

Therefore, the exterior angle x is 110°. This solution can be verified by noting that the exterior angle and its adjacent interior angle must sum to 180°. Indeed, 110° + 70° (the third interior angle, which can be calculated as 180° - 80° - 30°) equals 180°. This example illustrates how the Exterior Angle Theorem provides a direct method for solving equations involving triangle angles. It demonstrates the practical application of geometric theorems in problem-solving and reinforces the interconnectedness of algebraic and geometric concepts in mathematics.

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