Math Problem Statement

What is the measure of the third angle of a triangleif one angle measures 25° and the second angle measures 50°?

Solution

To find the measure of the third angle of a triangle, we use the triangle angle sum property, which states that the sum of the angles in a triangle is always 180180^\circ.

Calculation:

Let the angles of the triangle be AA, BB, and CC. We know: A+B+C=180A + B + C = 180^\circ Given: A=25,B=50A = 25^\circ, \quad B = 50^\circ

Substitute the known values: 25+50+C=18025^\circ + 50^\circ + C = 180^\circ

Simplify: 75+C=18075^\circ + C = 180^\circ

Solve for CC: C=18075=105C = 180^\circ - 75^\circ = 105^\circ

Final Answer:

The measure of the third angle is 105105^\circ.


Do you want more details or have any questions about this?
Here are 5 related questions to expand your understanding:

  1. How do you verify the sum of angles in a triangle using geometry?
  2. What happens if a triangle has one angle larger than 9090^\circ?
  3. How can the angle sum property be applied to solve problems in polygons other than triangles?
  4. What are the different types of triangles based on their angles (e.g., acute, obtuse)?
  5. How do you calculate the angles of a triangle when given their sides (using trigonometry)?

Tip: Always double-check your angle sum to ensure it equals 180180^\circ when working with triangles!

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Angle Sum

Formulas

Angle Sum Property: A + B + C = 180°

Theorems

Triangle Angle Sum Theorem

Suitable Grade Level

Grades 5-7