Math Problem Statement

If m∠ABD = 78°, what are m∠ABC and m∠DBC?

Solution

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We are given:

  • mABD=78m\angle ABD = 78^\circ
  • mABC=46m\angle ABC = 46^\circ
  • The expressions for angles:
    • DBC=(7x3)\angle DBC = (7x - 3)^\circ
    • DAB=(4x+4)\angle DAB = (4x + 4)^\circ

We need to find mDBCm\angle DBC.

Step-by-step Solution:

  1. Find mDBCm\angle DBC using given angles:

    Since mABD=mABC+mDBCm\angle ABD = m\angle ABC + m\angle DBC, we can write:

    78=46+mDBC78^\circ = 46^\circ + m\angle DBC

  2. Solve for mDBCm\angle DBC:

    mDBC=7846=32m\angle DBC = 78^\circ - 46^\circ = 32^\circ

Thus, mDBC=32m\angle DBC = 32^\circ.

Would you like more details or have any questions? Here are some related questions you might explore:

  1. What is the measure of DAB\angle DAB using the expressions given?
  2. How do you solve for xx using the expressions for DAB\angle DAB and DBC\angle DBC?
  3. What is the relationship between angles on a straight line?
  4. How can you verify if the given values are correct?
  5. How do supplementary angles relate to this problem?

Tip: When solving for unknowns, always check if there are multiple equations you can use to verify your solution.

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Math Problem Analysis

Mathematical Concepts

Geometry
Angle Calculation

Formulas

Sum of angles on a straight line

Theorems

Supplementary Angles Theorem

Suitable Grade Level

Grades 6-8