Math Problem Statement

Find the value of X

Find the value of X in the given geometric figure.

Solution

To find the value of xx in the given problem, we can use the properties of angles, specifically those related to vertical angles and the fact that the angles in a right angle must sum to 90°.

Step-by-Step Solution:

  1. Identify the given angles:

    • One angle is given as 4141^\circ.
    • Another angle is expressed as (11x23)(11x - 23)^\circ.
    • There is a right angle, which measures 9090^\circ.
  2. Recognize the relationships:

    • The two angles labeled 4141^\circ and (11x23)(11x - 23)^\circ are supplementary because they are adjacent and together form the right angle. This means:
    41+(11x23)=9041^\circ + (11x - 23)^\circ = 90^\circ
  3. Set up the equation:

    41+11x23=9041 + 11x - 23 = 90
  4. Simplify the equation:

    11x+18=9011x + 18 = 90
  5. Solve for xx:

    11x=901811x = 90 - 18 11x=7211x = 72 x=7211x = \frac{72}{11} x=6.5454(approximately)x = 6.5454 \quad (\text{approximately})

So, the value of xx is approximately 6.55.

Would you like more details on this solution or have any questions?

Here are 5 related questions you might find helpful:

  1. How do you find supplementary angles if one angle is unknown?
  2. What is the significance of vertical angles in geometry?
  3. How can you solve for xx when multiple angles are given in an equation?
  4. What is the relationship between adjacent angles and their sum?
  5. How do right angles influence the equations we set up for finding unknown variables?

Tip: Remember that angles on a straight line always add up to 180°, which can be very useful in solving various angle-related problems.

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Math Problem Analysis

Mathematical Concepts

Geometry
Algebra

Formulas

Sum of angles in a right angle (90°)
Equation for supplementary angles

Theorems

Angle Sum Theorem
Supplementary Angles

Suitable Grade Level

Grades 8-10