Math Problem Statement

Find the following x

Solution

To solve for xx in the provided image, I need to analyze each shape and the angles marked within them. Since the image contains quadrilaterals, I will use the fact that the sum of the interior angles in any quadrilateral is 360360^\circ. Let's break down each shape:

  1. Top-left quadrilateral:

    • The angles given are 7272^\circ, 118118^\circ, xx, and one unmarked angle.
    • The sum of the angles should be 360360^\circ.
    • Therefore, 72+118+x+unmarked angle=36072^\circ + 118^\circ + x + \text{unmarked angle} = 360^\circ.
  2. Top-right quadrilateral:

    • The angles given are xx, 107107^\circ, and 125125^\circ.
    • We can use a similar approach to find xx.
  3. Bottom-left quadrilateral:

    • The angles given are 142142^\circ, xx, and 108108^\circ.
    • Again, the sum should be 360360^\circ.

I'll start by analyzing each one to solve for xx. Let me extract the information step by step from the image.The solutions for xx in each quadrilateral depend on the unmarked fourth angle, denoted as angle4\text{angle}_4:

  1. Top-left quadrilateral: x=170angle4x = 170^\circ - \text{angle}_4
  2. Top-right quadrilateral: x=128angle4x = 128^\circ - \text{angle}_4
  3. Bottom-left quadrilateral: x=110angle4x = 110^\circ - \text{angle}_4

To determine the exact value of xx, the fourth angle (which is not provided in the image) is necessary. However, these expressions provide the relationship between xx and the unknown angle.

Would you like more details, or do you have any questions about the steps involved?

Here are 5 related questions that expand on the concepts:

  1. How do you calculate the sum of interior angles for any polygon?
  2. What are some properties of quadrilaterals that might help in solving these types of problems?
  3. How would you solve for xx if the fourth angle was given?
  4. What are the specific properties of parallelograms regarding their angles?
  5. How can you determine if a given quadrilateral is a specific type, like a trapezoid or a kite?

Tip: When solving for unknown angles in polygons, always ensure that you account for all angles and their relationships, especially when dealing with quadrilaterals or other polygons with complex angle arrangements.

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Math Problem Analysis

Mathematical Concepts

Geometry
Quadrilaterals
Interior Angles

Formulas

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Theorems

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Suitable Grade Level

High School