Solving Equations Using Triangle Properties: Example 6

Topic

Equations

Description

This example explores solving equations involving triangles that share a vertex at the center of a circle. We are presented with two equations: 

x + y = 75 and z + y = 110, where x, y, and z represent angles in the triangle

The goal is to solve this system of equations to find the values of x, y, and z, utilizing properties of isosceles triangles. Since each of the triangles is isosceles, we know that z + 55 + 55 = 180 and therefore, z = 70°. We substitute this into one of the equations:

70 + y = 110

7 = 40°

Now you can solve for x using the fact that these three angles form a 180° angle:

x + y + z = 180

x + 40 + 70 = 180

x = 70

This example demonstrates how algebraic techniques can be applied to solve geometric problems involving triangles inscribed in circles. It highlights the importance of understanding both the algebraic methods for solving systems of equations and the geometric properties of triangles and circles. This integration of algebra and geometry is a key aspect of mathematical problem-solving, showing how different areas of mathematics are interconnected and can be used together to solve complex problems.

For a complete collection of math examples related to Equations Using Triangle Properties click on this link: Math Examples: Equations Using Triangle Properties Collection.