Math Problem Statement

Find the value of x given that m∠ABD = 124°, m∠ABC = 52°, and m∠CBD = (6x + 6)°.

Solution

To find the value of xx, we will use the information provided in the image. The image gives us the following angles:

  1. mABD=124m\angle ABD = 124^\circ
  2. mABC=52m\angle ABC = 52^\circ
  3. mCBD=(6x+6)m\angle CBD = (6x + 6)^\circ

From the diagram, we can see that:

mABD=mABC+mCBDm\angle ABD = m\angle ABC + m\angle CBD

Substituting the given values:

124=52+(6x+6)124^\circ = 52^\circ + (6x + 6)^\circ

Now, let's solve for xx:

124=52+6x+6124 = 52 + 6x + 6

124=58+6x124 = 58 + 6x

12458=6x124 - 58 = 6x

66=6x66 = 6x

x=11x = 11

So, the value of xx is 1111.

Would you like further details or have any questions?

Here are some related questions that you might find interesting:

  1. How do you verify the value of xx using angle properties?
  2. What would be the value of mCBDm\angle CBD once xx is found?
  3. How would the problem change if mABCm\angle ABC was different?
  4. Can you calculate the supplementary angle to mABDm\angle ABD?
  5. How can you use these angle relationships to solve for unknowns in other geometric figures?

Tip: When solving for unknown variables in angles, always consider the relationships between angles, such as complementary, supplementary, or angles that form a straight line.

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Math Problem Analysis

Mathematical Concepts

Algebra
Angle Sum Property
Linear Pair

Formulas

m∠ABD = m∠ABC + m∠CBD

Theorems

Angle Sum Property
Linear Pair Theorem

Suitable Grade Level

Grades 7-9