Math Problem Statement

Find the value of the variables in the given figure: (8x - 10)°, (7x)°, and (6y + 20)°.

Solution

In this image, the problem involves finding the values of variables xx and yy based on angle relationships, likely involving parallel lines and transversals.

Here’s how we can approach it:

Step 1: Analyze the given angles

The figure shows two parallel lines with angles labeled as:

  • (8x10)(8x - 10)^\circ
  • (7x)(7x)^\circ
  • (6y+20)(6y + 20)^\circ

These angles seem to form corresponding, alternate interior, or supplementary angles depending on the configuration of the parallel lines.

Step 2: Set up equations based on angle relationships

  • If the angles (8x10)(8x - 10)^\circ and (7x)(7x)^\circ are on the same transversal and on opposite sides, they are likely alternate interior angles, which means: 8x10=7x8x - 10 = 7x Solve for xx: 8x7x=108x - 7x = 10 x=10x = 10

  • Now, substitute x=10x = 10 into the second equation involving yy. The angles (6y+20)(6y + 20)^\circ and (8x10)(8x - 10)^\circ seem to be supplementary (since they are on a straight line). This gives: (6y+20)+(8x10)=180(6y + 20) + (8x - 10) = 180 Substituting x=10x = 10: (6y+20)+(8(10)10)=180(6y + 20) + (8(10) - 10) = 180 (6y+20)+(8010)=180(6y + 20) + (80 - 10) = 180 6y+20+70=1806y + 20 + 70 = 180 6y+90=1806y + 90 = 180 6y=906y = 90 y=15y = 15

Step 3: Conclusion

The values of the variables are:

  • x=10x = 10
  • y=15y = 15

Would you like a further breakdown of the relationships between the angles?

Additional Questions:

  1. How do we determine when angles are alternate interior versus corresponding?
  2. Can you explain the difference between supplementary and complementary angles?
  3. Why do parallel lines create specific angle relationships with transversals?
  4. How do you apply these angle rules to real-world problems?
  5. What other types of angles can be formed when two lines are cut by a transversal?

Tip: Always remember to verify whether angles are supplementary, corresponding, or alternate interior by carefully analyzing the lines and transversals in geometry problems.

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Angles
Transversals
Parallel Lines

Formulas

Alternate interior angles are equal
Sum of supplementary angles is 180°

Theorems

Alternate Interior Angles Theorem
Supplementary Angles Theorem

Suitable Grade Level

Grades 8-10