Math Problem Statement

The measures of the angles of a triangle are shown in the figure below. Solve for x.

Solution

The image shows a triangle with two known angles: 36° and 83°. We are asked to find the unknown angle xx.

In any triangle, the sum of the interior angles is always 180°. Therefore, we can set up the following equation:

36+83+x=18036^\circ + 83^\circ + x^\circ = 180^\circ

Now, solving for xx:

x=180(36+83)x = 180^\circ - (36^\circ + 83^\circ)

x=180119=61x = 180^\circ - 119^\circ = 61^\circ

So, the value of xx is:

x=61x = 61^\circ

Would you like further details on the solution or have any additional questions?

Here are 5 related questions:

  1. What is the sum of the interior angles of any polygon with nn sides?
  2. How do you classify triangles based on their angles?
  3. Can a triangle have more than one obtuse angle?
  4. What is the exterior angle theorem for triangles?
  5. How do you find the missing angle in a right-angled triangle?

Tip: Always remember that the sum of the angles in a triangle is 180°, a key principle when solving for unknown angles.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles
Angle Sum Property

Formulas

Sum of the angles in a triangle: 180°

Theorems

Angle Sum Theorem

Suitable Grade Level

Grades 6-8