Math Problem Statement

Find the value of x in the diagram where angles 115° and 150° are given.

Solution

To solve this problem, we can use the property of a straight line: the sum of angles on a straight line is always 180°.

Step-by-step process:

  1. You are given that one angle is 150150^\circ and another is xx^\circ, both forming a straight line.

  2. The sum of the two angles must equal 180180^\circ.

    x+150=180x^\circ + 150^\circ = 180^\circ

  3. Solving for xx:

    x=180150=30x = 180^\circ - 150^\circ = 30^\circ

So, x=30x = 30^\circ.

Would you like more details, or do you have any questions?

Here are five related questions to expand your understanding:

  1. What is the sum of interior angles in any triangle?
  2. How do exterior angles of a triangle relate to interior angles?
  3. Can the sum of two angles ever exceed 180°? Why or why not?
  4. What is the angle sum property of polygons other than triangles?
  5. How would you apply the same method if you were given different angle values?

Tip: Always remember that angles on a straight line sum to 180180^\circ. This is called the linear pair property of angles.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles
Linear Pair

Formulas

x + 150° = 180°

Theorems

Linear Pair Theorem (angles on a straight line sum to 180°)

Suitable Grade Level

Grades 7-9