Math Problem Statement

Write a system of linear equations based on the trapezoid with given angle expressions: 2y°, 4x°, (2x + 12)°, and (y + 6)°.

Solution

To solve this problem, we need to understand the properties of the angles in a trapezoid. In a trapezoid, the angles on the same side (called consecutive angles) are supplementary, meaning their measures add up to 180180^\circ.

Here, we have four angles given as 2y2y^\circ, 4x4x^\circ, (2x+12)(2x + 12)^\circ, and (y+6)(y + 6)^\circ.

We can set up equations based on the fact that the angles on the same side are supplementary:

  1. The angles 2y2y^\circ and (2x+12)(2x + 12)^\circ are on the same side, so: 2y+(2x+12)=1802y + (2x + 12) = 180

  2. The angles 4x4x^\circ and (y+6)(y + 6)^\circ are also on the same side, so: 4x+(y+6)=1804x + (y + 6) = 180

These two equations can be written as:

  • Equation 1: 2y+2x+12=1802y + 2x + 12 = 180
  • Equation 2: 4x+y+6=1804x + y + 6 = 180

You can simplify these equations further if needed:

  • Simplifying Equation 1: 2x+2y=1682x + 2y = 168
  • Simplifying Equation 2: 4x+y=1744x + y = 174

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

  1. How can you solve the system of linear equations obtained here?
  2. What would the solution represent in the context of the angles in the trapezoid?
  3. How do properties of trapezoids help in forming these equations?
  4. What methods can be used to solve a system of two linear equations?
  5. How would the problem change if we were dealing with a different type of quadrilateral?

Tip: Remember, supplementary angles add up to 180180^\circ. This property is very useful in problems involving polygons.

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations
Properties of Trapezoids
Supplementary Angles

Formulas

Supplementary angles: angle1 + angle2 = 180°

Theorems

Consecutive angles in a trapezoid are supplementary.

Suitable Grade Level

Grades 7-9