Math Problem Statement

Solve for angle x in the diagram where one angle is 95°, another angle is 60°, and the intersecting lines create supplementary and vertical angles.

Solution

To solve for the value of angle xx in the provided diagram, let's break this down step by step:

Analyzing the Given Information

  1. The diagram shows intersecting lines, creating vertical and supplementary angles.
  2. Given angles:
    • One angle is 9595^\circ.
    • Adjacent to it, there is an angle of 6060^\circ.
    • The angle xx needs to be determined.

Using Geometrical Relationships

  1. Angles on a straight line: When two angles share a straight line, their sum is 180180^\circ because they are supplementary angles.

  2. Vertical angles: Angles opposite each other at the intersection of two lines are equal.


Solving for xx:

  • The angle adjacent to 9595^\circ and 6060^\circ forms a straight line. Therefore: Adjacent angle=18095=85\text{Adjacent angle} = 180^\circ - 95^\circ = 85^\circ

  • Now, angle xx and 6060^\circ also form a straight line. Hence: x+60=180x + 60^\circ = 180^\circ

  • Solving for xx: x=18060=120x = 180^\circ - 60^\circ = 120^\circ


Final Answer:

The value of xx is 120120^\circ.

Let me know if you'd like further clarification or additional details! Here are related questions you may find useful:

  1. How do supplementary and vertical angles relate to intersecting lines?
  2. What are alternate interior angles and how are they used in solving geometry problems?
  3. Can you explain the angle sum property of a triangle?
  4. How can you determine missing angles when two parallel lines are cut by a transversal?
  5. What is the difference between complementary and supplementary angles?

Tip: Always look for straight-line relationships or opposite (vertical) angles when solving for unknown angles in intersecting line diagrams.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles formed by intersecting lines
Supplementary angles
Vertical angles

Formulas

Supplementary angles: a + b = 180°
Vertical angles are equal

Theorems

Supplementary Angles Theorem
Vertical Angles Theorem

Suitable Grade Level

Grades 8-10