Math Problem Statement

The measures of the angles of a triangle are shown in the figure. Solve for x given the angles: 75°, 42°, and (8x + 15)°.

Solution

The value of xx is 6.

Would you like more details on how this was solved or have any further questions?

Here are 5 related questions to deepen your understanding:

  1. How can the sum of the angles in a triangle be proven to always equal 180°?
  2. What happens to the values of the angles if xx increases or decreases?
  3. Can this method be used to solve for variables in other polygons' interior angles?
  4. How would you solve for the side lengths of the triangle if they were given in terms of xx?
  5. How can trigonometry help when only two angles of a triangle are known?

Tip: Always check the sum of angles in any polygon using known formulas. For triangles, the angles always sum up to 180°.

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Math Problem Analysis

Mathematical Concepts

Geometry
Algebra
Angle Sum Property

Formulas

Sum of angles in a triangle: 180°

Theorems

Sum of Interior Angles Theorem

Suitable Grade Level

Grades 7-9