Math Problem Statement

Find the value of the varibles

Find the values of the variables based on the given angles in the intersecting lines diagram.

Solution

The image shows two intersecting lines that form angles labeled xx^\circ, yy^\circ, and 9y9y^\circ. These angles are connected by properties of vertical and adjacent angles.

Step 1: Identify relationships between the angles

  • The angles xx^\circ and yy^\circ are vertical angles, so they are equal: x=yx = y

  • The angles yy^\circ and 9y9y^\circ are on a straight line, which means they are supplementary (their sum is 180°): y+9y=180y + 9y = 180

Step 2: Solve for yy

y+9y=180y + 9y = 180 10y=18010y = 180 y=18010=18y = \frac{180}{10} = 18

Step 3: Solve for xx

Since x=yx = y, we also have: x=18x = 18

Final Answer:

  • x=18x = 18
  • y=18y = 18

Would you like further explanation on any step or more details?


Here are some related questions for deeper understanding:

  1. What are supplementary angles, and how do they apply here?
  2. Why are vertical angles equal?
  3. Can you explain the difference between supplementary and complementary angles?
  4. What is the significance of intersecting lines in geometry?
  5. How would this problem change if one of the angles were missing?

Tip: Always remember, vertical angles formed by intersecting lines are congruent!

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles
Vertical Angles
Supplementary Angles

Formulas

Vertical angles are congruent (equal)
Supplementary angles add up to 180 degrees

Theorems

Vertical Angles Theorem
Supplementary Angles Theorem

Suitable Grade Level

Grades 6-8