Math Problem Statement

Calculate the value of x using the given geometric diagram.

Solution

The image contains a geometric diagram and a question that asks to calculate the value of xx.

The diagram shows a straight line with points labeled AA, BB, and CC. There is a line extending from point BB to point DD, forming an angle at point BB. There is a 90° angle between line segments ABAB and BDBD, and an indicated angle DBC=52\angle DBC = 52^\circ.

To calculate xx, which appears to be the unknown angle ABC\angle ABC, we can use the following reasoning:

Solution:

  1. Since ABAB and BDBD form a 90° angle, the total angle on the straight line at point BB must be 180° (because angles on a straight line sum up to 180°).
  2. The angle DBC\angle DBC is given as 5252^\circ.
  3. Therefore, ABC\angle ABC is calculated by subtracting the sum of the known angles from 180°: x=1809052=38.x = 180^\circ - 90^\circ - 52^\circ = 38^\circ.

Thus, the value of xx is 3838^\circ.


Do you have any further questions or would you like more details on this solution? Here are some related questions you might find helpful:

  1. What is the sum of angles in a triangle?
  2. How do complementary and supplementary angles differ?
  3. How can you use the sine, cosine, and tangent functions in right triangles?
  4. What are the angle properties in parallel lines intersected by a transversal?
  5. How do you calculate unknown angles in different types of polygons?

Tip: When dealing with straight lines and angles, remember that the sum of angles on a straight line is always 180°.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angles on a Straight Line

Formulas

Sum of angles on a straight line = 180°

Theorems

Angle Sum Property on a Straight Line
Complementary Angles

Suitable Grade Level

Grades 6-8