Math Problem Statement

Find the measure of the missing angles. The diagram shows an angle of 123° with two unknown angles b and c.

Solution

The image shows a problem related to vertical, adjacent, and complementary angles. The diagram has an angle labeled as 123° and two unknown angles, bb and cc, that you need to find.

Step-by-step solution:

  1. Identifying the angles:

    • Angle bb and the 123° angle are vertical angles, meaning they are equal. b=123b = 123^\circ
  2. Finding angle cc:

    • Angle cc and the 123° angle are adjacent angles forming a straight line, meaning they are supplementary. The sum of supplementary angles is 180°. c+123=180c + 123^\circ = 180^\circ Solving for cc: c=180123=57c = 180^\circ - 123^\circ = 57^\circ

Final Answer:

  • b=123b = 123^\circ
  • c=57c = 57^\circ

Would you like further details on this solution or clarification on any part?

Here are 5 related questions to explore further:

  1. What are complementary angles, and how do they differ from supplementary angles?
  2. How do vertical angles relate to each other in different geometric configurations?
  3. Can two adjacent angles ever be complementary? If so, under what conditions?
  4. How can you determine if a set of angles forms a linear pair?
  5. What is the difference between adjacent and non-adjacent supplementary angles?

Tip: When dealing with angles around a point or straight lines, always check for vertical and supplementary angle relationships!

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Math Problem Analysis

Mathematical Concepts

Geometry
Vertical Angles
Adjacent Angles
Supplementary Angles

Formulas

Vertical angles are equal: b = 123°
Supplementary angles add up to 180°: c + 123° = 180°

Theorems

Vertical Angles Theorem
Supplementary Angles Theorem

Suitable Grade Level

Grades 6-8