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Math Example--Solving Equations--Solving Equations Using Angle Properties: Example 6

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# Solving Equations Using Angle Properties: Example 6

## Topic

Equations

## Description

This example illustrates solving equations using angle properties, focusing on an isosceles right triangle. An isosceles right triangle has a right angle (90°) and two equal angles. In this scenario, we have the right angle given, and the two unknown equal angles represented by x.

The equation can be set up based on the fact that the sum of angles in a triangle is 180°. Thus, we have:

90 + x + x = 180, or simplified, 90 + 2x = 180

To solve for x, we first subtract 90 from both sides: 2x = 90. Then, dividing both sides by 2, we get: x = 45°.

This method of solving angle equations relies on understanding multiple geometric properties and applying basic algebraic techniques. It's essential to recognize various properties of special triangles, such as isosceles triangles and right triangles. By identifying these properties, we can formulate equations and solve for unknown angles. This process not only reinforces geometric concepts but also strengthens algebraic problem-solving skills. In practical applications, such problems are crucial in fields like architecture, engineering, and computer graphics, where understanding and calculating angles in special triangles is necessary for structural design, efficient algorithms, and creating accurate visual representations.

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

Common Core Standards | CCSS.MATH.CONTENT.HSG.CO.C.10, CCSS.MATH.CONTENT.HSA.CED.A.1 |
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Grade Range | 9 - 11 |

Curriculum Nodes |
Algebra• Expressions, Equations, and Inequalities• Applications of Equations and InequalitiesGeometry• Angles and Planes• Definition of an Angle |

Copyright Year | 2022 |

Keywords | angles, solving equations |