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:

120°

Step-by-step 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°.

19.side- angle- side

20. angle- side- angle

step-by-step explanation: