Math Problem Statement

Solve for X in a triangle where one angle is 120 degrees, and two smaller angles are 3X and 2X degrees respectively.

Solution

The diagram shows a triangle with several given angles. To solve for XX, we need to use angle properties of triangles.

Step 1: Analyze the big triangle

In the large triangle, one angle is given as 120120^\circ (marked in purple). The triangle is split into two smaller triangles by two lines, and these triangles each have one of the angles marked as 3X3X^\circ and 2X2X^\circ.

Step 2: Use the fact that the sum of angles in any triangle is 180180^\circ

In the smaller right triangle on the right side, the angles are 2X2X^\circ and XX^\circ, and the third angle (external to this triangle) is part of the overall triangle structure. We need to calculate it by setting up equations based on angle sums and properties.

Step 3: Solve for XX

We will set up a relationship between XX, 3X3X, and other known angle properties. I'll proceed to solve this.The value of XX is 1010^\circ.

Would you like a more detailed explanation, or do you have any questions?

Here are 5 related questions to expand your understanding:

  1. How do we apply the sum of angles in a triangle in different types of problems?
  2. What is the role of external angles in geometry?
  3. Can you identify different types of triangles based on their angles?
  4. How do angle bisectors affect the properties of a triangle?
  5. How do supplementary angles help in solving triangle-related problems?

Tip: Always remember that the sum of interior angles in any triangle is 180180^\circ, and this property can be very helpful in solving geometric problems.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Angle Sum Property of Triangles
Equations

Formulas

Sum of angles in a triangle = 180°

Theorems

Angle Sum Property
Linear Pair Theorem

Suitable Grade Level

Grades 7-10