Math Problem Statement

Determine with reasons the value of the angles G and L in triangles EFG and KLM.

Solution

Let's analyze the problem given in the diagram.

Step 1: Identify what is known

In the diagram:

  • In triangle EFG\triangle EFG:

    • E=40\angle E = 40^\circ
    • F=100\angle F = 100^\circ
  • In triangle KLM\triangle KLM:

    • K=40\angle K = 40^\circ
    • L=40\angle L = 40^\circ

Step 2: Apply triangle angle sum property

The sum of angles in a triangle is always 180180^\circ. We can use this to determine the unknown angles.

  1. Determine G\angle G in EFG\triangle EFG:

    • The sum of angles in a triangle is 180180^\circ, so: G=180(E+F)\angle G = 180^\circ - ( \angle E + \angle F ) G=180(40+100)=180140=40\angle G = 180^\circ - (40^\circ + 100^\circ) = 180^\circ - 140^\circ = 40^\circ So, G=40\angle G = 40^\circ.
  2. Determine M\angle M in KLM\triangle KLM:

    • Similarly, using the angle sum property in KLM\triangle KLM: M=180(K+L)\angle M = 180^\circ - ( \angle K + \angle L ) M=180(40+40)=18080=100\angle M = 180^\circ - (40^\circ + 40^\circ) = 180^\circ - 80^\circ = 100^\circ So, M=100\angle M = 100^\circ.

Thus, we have determined:

  • G=40\angle G = 40^\circ
  • L=40\angle L = 40^\circ (already given).

Do you need further explanation or details about these steps?

Here are 5 related questions to help deepen understanding:

  1. What is the sum of angles in any triangle, and why is it always 180180^\circ?
  2. How do corresponding angles work when triangles are parallel?
  3. Can two triangles be similar if only their

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles
Angle Sum Property

Formulas

Sum of angles in a triangle: ∠A + ∠B + ∠C = 180°

Theorems

Triangle Angle Sum Theorem

Suitable Grade Level

Grade 8-10