Math Problem Statement

Find the value of x in the given triangle with angles 36°, 110°, and x°.

Solution

The image depicts a triangle with two known angles, 36° and 110°, along with an unknown angle xx^\circ that needs to be found.

To solve for xx:

  1. Sum of interior angles in a triangle: The sum of the interior angles of any triangle is always 180°. In this case, the three angles are 3636^\circ, 110110^\circ, and xx^\circ.

We can set up the equation: 36+110+x=18036^\circ + 110^\circ + x = 180^\circ

  1. Solving for xx: x=180(36+110)=180146=34x = 180^\circ - (36^\circ + 110^\circ) = 180^\circ - 146^\circ = 34^\circ

Thus, the value of xx is 34\boxed{34^\circ}.

Do you want any more details or have further questions?

Here are five related questions:

  1. What is the sum of the exterior angles of a triangle?
  2. How can you classify a triangle based on its angles?
  3. What are the properties of an isosceles triangle?
  4. Can a triangle have two obtuse angles? Why or why not?
  5. What happens if the sum of two angles in a triangle exceeds 180°?

Tip: Always double-check your calculations in geometry by verifying angle sums, especially in triangles!

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles in a Triangle

Formulas

Sum of angles in a triangle: 36° + 110° + x = 180°

Theorems

Triangle Sum Theorem

Suitable Grade Level

Grades 6-8