Math Problem Statement

Based on the diagram below, find the value of x. The angles of the triangle are: x + 25°, 3x + 2°, and x + 17°.

Solution

In this problem, we are asked to find the value of xx based on the angles in the given triangle. The triangle's angles are expressed as follows:

  • One angle: x+25x + 25^\circ
  • Another angle: 3x+23x + 2^\circ
  • The third angle: x+17x + 17^\circ

Step-by-step solution:

  1. Sum of angles in a triangle: The sum of the interior angles of any triangle is always 180180^\circ.

    (x+25)+(3x+2)+(x+17)=180(x + 25^\circ) + (3x + 2^\circ) + (x + 17^\circ) = 180^\circ

  2. Simplify the equation:

    x+25+3x+2+x+17=180x + 25 + 3x + 2 + x + 17 = 180

    Combine like terms:

    5x+44=1805x + 44 = 180

  3. Solve for xx:

    Subtract 44 from both sides:

    5x=1365x = 136

    Now, divide by 5:

    x=27.2x = 27.2

Therefore, the value of xx is 27.227.2^\circ.


Would you like more details on this solution or have any questions? Here are five related problems to explore further:

  1. If one angle in a triangle is known, how do you find the other two angles?
  2. How does the exterior angle theorem apply in triangle angle problems?
  3. If one angle of a triangle is right, how does that change the sum of the other angles?
  4. How do the properties of an equilateral triangle affect its angles?
  5. Can triangles have angles expressed with different variables? How would you approach solving that?

Tip: Always check if all given angles sum to 180°, as this is a key property of triangles.

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Math Problem Analysis

Mathematical Concepts

Geometry
Algebra

Formulas

Sum of interior angles in a triangle = 180°

Theorems

Triangle Angle Sum Theorem

Suitable Grade Level

Grades 8-10