Math Problem Statement

Find the measure of angle b in a triangle where one angle is given as 123°, and another angle is part of a right triangle setup.

Solution

This is a triangle where one of the angles is given as 123123^\circ, and the task is to find the measure of angle bb. Since no information about the other angles or sides is provided, we assume this is a triangle and use the Triangle Sum Theorem, which states that the sum of all angles in a triangle is 180180^\circ.

Solution:

  1. Denote the three angles of the triangle as:

    • 123123^\circ (given),
    • bb (unknown, to be found),
    • A third angle we'll call cc.
  2. The sum of all angles in a triangle is 180180^\circ: 123+b+c=180123^\circ + b + c = 180^\circ

  3. Notice that angle cc is a right angle (9090^\circ) because the triangle has a right angle in its diagram.

  4. Substitute c=90c = 90^\circ into the equation: 123+b+90=180123^\circ + b + 90^\circ = 180^\circ

  5. Simplify: 213+b=180213^\circ + b = 180^\circ

  6. Solve for bb: b=180213b = 180^\circ - 213^\circ b=33b = -33^\circ


This suggests an inconsistency, likely a misinterpretation of the triangle's setup. For clarity:

  1. Verify whether the diagram correctly intends a right angle, or if more detail is required to find bb.
  2. Ask for clarification if needed.

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Math Problem Analysis

Mathematical Concepts

Triangle Sum Theorem
Angles in Triangles

Formulas

Sum of angles in a triangle = 180°

Theorems

Triangle Sum Theorem

Suitable Grade Level

Grades 6-8