Math Problem Statement

Find the value of x in the triangle where two angles are 33° and 31°.

Solution

To solve for xx in this triangle, we use the basic property of triangles that states:

The sum of all interior angles in a triangle equals 180180^\circ.

The angles given are:

  • 3333^\circ (bottom left),
  • 3131^\circ (bottom right),
  • xx^\circ (top angle).

Thus, we can set up the equation: x+33+31=180x + 33 + 31 = 180

Solve for xx:

x+64=180x + 64 = 180 x=18064x = 180 - 64 x=116x = 116^\circ

Final Answer:

x=116x = 116^\circ

Let me know if you'd like a further explanation or need help with related problems!


Related Questions:

  1. What are the properties of the sum of angles in polygons?
  2. How do you determine unknown angles in an isosceles triangle?
  3. How can you use exterior angles to calculate interior angles?
  4. What is the triangle inequality theorem?
  5. How do you classify triangles based on angles?

Tip:

Always check your answers by verifying the sum of the angles equals 180180^\circ.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Properties
Angle Sum in a Triangle

Formulas

Sum of interior angles in a triangle = 180°

Theorems

Angle Sum Property of a Triangle

Suitable Grade Level

Grades 6-8