Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 3
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Algebra >> Expressions, Equations, and Inequalities >> Solving Multistep Equations

Math Example--Solving Equations--Solving Equations with Angle Measures 2--Example 3

Solving Equations with Angle Measures 2--Example 3

Trapezoid with angles 75°, 80°, x°, and y°

Topic

Equations

Description

This example demonstrates solving equations involving angle measures in a trapezoid. The trapezoid has two known angles of 75° and 80°, and two unknown angles x° and y°. To solve this problem, we apply two key principles: the sum of angles in a quadrilateral is 360°, and the angles on the same side of a transversal are supplementary. We can set up two equations: 75° + 80° + x° + y° = 360° and 80° + y° = 180°. From the second equation, we can deduce that y° = 100°. Substituting this into the first equation: 75° + 80° + x° + 100° = 360°. Simplifying, we get x° = 105°. This problem showcases how to solve systems of equations in geometric contexts. It reinforces the understanding of trapezoid properties and helps students develop skills in translating complex geometric relationships into multiple algebraic equations. Such problems are crucial in developing analytical thinking and preparing students for more advanced concepts in geometry and algebra.

For a complete collection of math examples related to Solving Equations with Angle Measures click on this link: Math Examples: Solving Equations with Angle Measures Collection.

Common Core Standards CCSS.MATH.CONTENT.8.G.A.5, CCSS.MATH.CONTENT.HSG.CO.C.10, CCSS.MATH.CONTENT.7.EE.B.4.A, CCSS.MATH.CONTENT.7.G.B.5
Grade Range 8 - 10
Curriculum Nodes Algebra
    • Expressions, Equations, and Inequalities
        • Solving Multistep Equations
Geometry
    • Quadrilaterals
        • Applications of Quadrilaterals
Copyright Year 2020
Keywords quadrilaterals, equations