Math Problem Statement

Given the angles in the image, find the equation and the measures of angles ABD and DBC.

Solution

The diagram shows two angles sharing a vertex BB. You have two labeled angles: one is 2x2x^\circ and the other is 3x3x^\circ. These two angles appear to form a linear pair because their sum is a straight line, which measures 180180^\circ.

Step-by-step solution:

  1. Equation for angle sum: Since angles ABD\angle ABD (measuring 2x2x^\circ) and DBC\angle DBC (measuring 3x3x^\circ) form a straight line, the sum of these two angles should equal 180180^\circ. So, the equation is: 2x+3x=1802x + 3x = 180

  2. Solving for xx: 5x=1805x = 180 x=1805=36x = \frac{180}{5} = 36

  3. Measure of ABD\angle ABD: Since ABD=2x\angle ABD = 2x: ABD=2(36)=72\angle ABD = 2(36) = 72^\circ

  4. Measure of DBC\angle DBC: Since DBC=3x\angle DBC = 3x: DBC=3(36)=108\angle DBC = 3(36) = 108^\circ

Answers:

  • Equation: 2x+3x=1802x + 3x = 180
  • x=36x = 36
  • mABD=72m \angle ABD = 72^\circ
  • mDBC=108m \angle DBC = 108^\circ

Would you like further explanation on any step, or have any additional questions? Here are 5 related questions that might help deepen understanding:

  1. What are the characteristics of a linear pair of angles?
  2. How do you verify that two angles form a straight line?
  3. Can two angles have different measures but still add up to 180180^\circ?
  4. How do complementary angles differ from supplementary angles?
  5. If one of the angles were 4x4x instead of 3x3x, how would the solution change?

Tip: For any angles that form a straight line, their sum will always be 180180^\circ.

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Math Problem Analysis

Mathematical Concepts

Geometry
Linear Pairs
Angle Relationships

Formulas

Sum of angles on a straight line: angle1 + angle2 = 180°

Theorems

Linear Pair Postulate

Suitable Grade Level

Grades 6-8