Math Problem Statement

Find x. Lines AB and CD intersect at O with angles 3x, x, x + 12°, and 152° at the point of intersection.

Solution

To find xx in the given diagram, let's analyze the angle relationships at point OO where lines ABAB and CDCD intersect.

  1. Since lines intersect, opposite angles are equal (also known as vertically opposite angles). We have: 3x=1523x = 152^\circ

  2. Solving for xx from this equation: x=1523=50.67x = \frac{152^\circ}{3} = 50.67^\circ

  3. Now, substitute x=50.67x = 50.67^\circ into the expression x+12x + 12^\circ to verify consistency with other angles in the setup.

  4. Therefore, x50.67x \approx 50.67^\circ, based on the given angles and the properties of intersecting lines.

If you need further clarification on any of the steps, please let me know!


Would you like more details on this solution or have any questions?

Here are some related questions to further your understanding:

  1. How are vertically opposite angles defined in geometry?
  2. Why do intersecting lines create equal opposite angles?
  3. How would the solution change if AOD\angle AOD was not given as 152152^\circ?
  4. Can you find other angle values in the diagram given x50.67x \approx 50.67^\circ?
  5. What other methods can be used to solve for unknown angles in intersecting line diagrams?

Tip: In intersecting lines, opposite angles are always equal. This property is very useful in finding unknown angles.

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Math Problem Analysis

Mathematical Concepts

Angle Properties
Linear Equations
Geometry

Formulas

Vertically Opposite Angles are Equal

Theorems

Vertically Opposite Angles Theorem

Suitable Grade Level

Grades 8-10