Solving Equations Using Angle Properties: Example 4

Equations

Description

This example illustrates solving equations using angle properties, focusing on straight angles and vertical angles. A straight angle measures 180°, and vertical angles are always congruent. In this scenario, we have two known angles (42° and 55°) and an unknown angle x. However, angle x is vertical (and therefore congruent) to angle y.

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

42 + 55 + x = 180

To solve for x, we first add the known angles: 97 + x = 180. Then, subtracting 97 from both sides, we get: x = 83°.

This method of solving angle equations relies on understanding multiple geometric properties and applying basic algebraic techniques. It's essential to recognize various angle relationships in geometry, such as straight angles and vertical angles. By identifying these relationships, 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-aided design, where precise angle calculations are necessary for structural integrity, efficient design, and accurate modeling.

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 9 - 11 Algebra     • Expressions, Equations, and Inequalities         • Applications of Equations and Inequalities Geometry     • Angles and Planes         • Definition of an Angle 2022 angles, solving equations