Math Problem Statement

En la siguiente figura halle el valor de x: 36° + (50 - 2)° + (2x - 1)° = 180°

Solution

The image shows a geometric figure with a problem asking to find the value of xx based on the angles given in the figure. Here's a step-by-step approach to solve the problem:

  1. Identify the relationships between angles:

    • The top-left corner has a given angle of 36°.
    • There’s another angle labeled 50250 - 2 (which simplifies to 48°).
    • The last angle is expressed as 2x12x - 1, meaning we need to solve for xx.
  2. Utilize the angle relationships: The three angles shown in the figure form a straight line (linear pair), meaning their sum must equal 180°.

    Therefore, the equation becomes: 36+(502)+(2x1)=18036 + (50 - 2) + (2x - 1) = 180 Simplifying: 36+48+(2x1)=18036 + 48 + (2x - 1) = 180 83+2x1=18083 + 2x - 1 = 180 82+2x=18082 + 2x = 180 2x=180822x = 180 - 82 2x=982x = 98 x=982=49x = \frac{98}{2} = 49

Thus, x=49x = 49.

Since none of the provided answers seem to match this solution (the choices are fractions or decimals), the correct answer is likely e) Ninguna (None of the above).

Would you like more details or have any questions?


Relative questions:

  1. What is the definition of a linear pair of angles?
  2. How do you verify the sum of angles in a straight line?
  3. Can angles formed by intersecting lines be calculated using other properties?
  4. What happens if the angles do not sum to 180° in such problems?
  5. How do you solve equations that involve multiple variables in geometry?

Tip: Always double-check angle relationships in geometry, especially when dealing with supplementary or complementary angles.

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Math Problem Analysis

Mathematical Concepts

Geometry
Linear Pair of Angles

Formulas

Sum of angles on a straight line equals 180°

Theorems

Linear Pair Theorem

Suitable Grade Level

Grade 8-10