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Every triangle in the figure at right is equilateral. What is the measure of ∠AGE?

Step:

1. Use the corollaries of the isosceles triangle theorem. Each angle in an equilateral triangle measures 60° 2. Use those two angles to find m∠AGE.

Problem:

Every triangle in the figure at right is equilateral. What is the measure of ∠AGE-example-1
Every triangle in the figure at right is equilateral. What is the measure of ∠AGE-example-1
Every triangle in the figure at right is equilateral. What is the measure of ∠AGE-example-2
Every triangle in the figure at right is equilateral. What is the measure of ∠AGE-example-3
User Harryisaac
by
5.3k points

1 Answer

7 votes

Answer:

120°

Explanation:

All the angles of an equilateral triangle are equal, and hence have a measure of 60°.

∵ ∠AGF is a part of equilateral Δ AGF, m∠AGF = 60°.

∵ ∠FGE is a part of equilateral Δ AGF, m∠FGE = 60°.

Also note that ∠AGE = ∠AGF + ∠FGE.

m∠AGE = m∠AGF + m∠FGE

m∠AGE = 60° + 60°

= 120°.

User Rlarcombe
by
4.0k points