Math Problem Statement

Which angle in triangle DEF has the largest measure? Given that side DF = 6, side EF = 7, and side DE = 11.

Solution

To determine which angle in triangle DEF\triangle DEF has the largest measure, we can use the property of triangles that states:

In a triangle, the largest angle is opposite the longest side.

From the diagram:

  • Side DFDF has a length of 6,
  • Side EFEF has a length of 7,
  • Side DEDE has a length of 11.

Since DE=11DE = 11 is the longest side, the angle opposite this side is F\angle F.

Therefore, F\angle F is the largest angle in triangle DEFDEF.

The correct answer is C. F\angle F.

Would you like further clarification or have any questions?

Here are 5 related questions:

  1. How can the Law of Cosines be used to find specific angles in a triangle?
  2. What are the other properties of a triangle related to angle and side measures?
  3. How do the angles of a triangle sum up, and how is this fact used in problems?
  4. Can we determine specific angle measures without using side lengths?
  5. What is the relationship between an equilateral triangle’s sides and angles?

Tip: In any triangle, the angle opposite the longest side will always be the largest.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangle Properties

Formulas

In a triangle, the largest angle is opposite the longest side.

Theorems

Triangle Inequality Theorem
Properties of Triangles

Suitable Grade Level

Grades 6-8