Solving Equations Using Triangle Properties: Example 9

Topic

Equations

Description

This example focuses on solving equations using the properties of a kite and applying the exterior angle theorem. We are given one angle of 30° 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 diagonals of a kite are perpendicular. 
• 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°. 

Do you see that x and y are base angles of corresponding isosceles triangles? We can use that property to solve for y:

y + y + 30 = 180

y = 75°

We can now solve for x:

x + y = 135

x + 75 = 135

x = 60°

This example demonstrates the application of multiple geometric concepts, including properties of kites and the exterior angle theorem, to solve a system of equations. It highlights the importance of understanding the unique properties of specific quadrilaterals and how these properties can be used in conjunction with general triangle theorems to solve complex problems. The problem also illustrates the power of algebraic methods in geometry, showing how equations can be set up and solved based on geometric relationships.

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