Solving Equations Using Triangle Properties: Example 10

Topic

Equations

Description

This example, similar to Example 9, involves solving equations using the properties of a kite and applying the exterior angle theorem. We are again given one angle of 40° and two unknown angles, y and x. The goal is to set up and solve equations to find the values of y and x using the properties of kites and the exterior angle theorem. 

Key properties to consider: 

• In a kite, two pairs of adjacent sides are equal. 
• The angles opposite the equal sides in a kite are equal. 
• The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. 
• The sum of angles in a triangle is 180°. 

To solve this problem, we follow the same steps as in Example 9: Use the properties of isosceles triangles. First solve for y:

y + y + 40 = 180

y = 70°

We can now solve for z, using the given information:

y + z = 148

70 + z = 148

z = 78°

We can now solve for x using the properties of isosceles triangles:

x + 78 + 78 = 180

x = 24°

This example reinforces the concepts demonstrated in Example 9, showing how the same geometric principles can be applied consistently to solve similar problems. It emphasizes the importance of understanding the properties of kites and how they interact with general triangle theorems like the exterior angle theorem. The problem also highlights the systematic approach to solving geometric equations, demonstrating how algebraic methods can be effectively used to solve geometric problems. By presenting a similar problem with the same solution, this example also illustrates the concept of multiple representations in geometry, where different diagrams can lead to the same mathematical relationships and solutions.

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