Math Problem Statement

In the given figure, AB || CD. Find the value of x.

Solution

We are given a diagram where ABCDAB \parallel CD, and we need to find the value of angle xx. Let's break this down:

Step 1: Parallel Lines and Corresponding Angles

Since ABCDAB \parallel CD and the transversal is AEAE, the angle AEB=20\angle AEB = 20^\circ and CDE=130\angle CDE = 130^\circ are related to the angles at AA and CC.

  • The angle BAE\angle BAE is formed between the transversal AEAE and the line ABAB. Therefore, by the corresponding angles theorem (because ABCDAB \parallel CD), the angle at AA corresponding to CDE\angle CDE will be 130130^\circ as well.

Step 2: Angles in a Triangle

Now, looking at triangle AECAEC, we know that the sum of the internal angles of any triangle is 180180^\circ. In this triangle, we have:

  • AEB=20\angle AEB = 20^\circ (given),
  • CED=130\angle CED = 130^\circ,
  • And the angle xx at AA is what we need to find.

The sum of these angles should equal 180180^\circ: x+130+20=180x + 130^\circ + 20^\circ = 180^\circ

Step 3: Solving for xx

x+150=180x + 150^\circ = 180^\circ x=180150x = 180^\circ - 150^\circ x=30x = 30^\circ

Thus, the value of xx is 3030^\circ.

Would you like any further clarifications or additional details?

Here are some related questions to expand your understanding:

  1. How do corresponding angles help in parallel line problems?
  2. Can you apply the concept of alternate interior angles to this problem?
  3. How would the calculation change if angle CED\angle CED was different?
  4. What are other ways to find angles in geometrical shapes involving parallel lines?
  5. Can you explore how to solve such problems in 3D geometry?

Tip: Always remember that the sum of the angles in a triangle is 180180^\circ, which is fundamental in solving many geometrical problems!

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Math Problem Analysis

Mathematical Concepts

Geometry
Parallel Lines
Angles
Triangle Sum Property

Formulas

Sum of angles in a triangle = 180°

Theorems

Corresponding Angles Theorem
Triangle Angle Sum Theorem

Suitable Grade Level

Grades 7-9