Isosceles and Equilateral sides with Algebra

If ( ABC ) is an equilateral triangle, solve for both ( x ) and ( y ).​ ​ ​

If ( RST ) is an equilateral triangle, find the measure of each side.

If ( MNP ) is an equilateral triangle, find the measure of each side.

If ( DEF ) is an isosceles triangle with ( DE ) congruent to ( EF ), find ( x )

If ( WXY ) is an isosceles triangle with ( WX ) congruent to ( XY ), find the measure of ( WY ).

If ΔPQR is an equilateral triangle, PQ = 18x + 1, QR = 24x – 17, and PR = 15x + 10, find the measure of each side.

ΔSTU is an equilateral triangle. If ST is one less than twice x, SU is 37 less than five times x, and TU is 11 more than x, find the measure of each side.

ΔMKL is an isosceles triangle with MK ≅ ML. If MK = 7x – 15, KL = 4x – 5, and ML = 10x – 42, find the measure of ( KL ).

ΔABC is an isosceles triangle with AB ≅ BC. If AB = 3x + 41, BC = 8x – 54, and AC = 12x – 103, find the measure of ( AC ).

ΔGHI is an isosceles triangle with GI ≅ HI. If GH is three more than x, HI is 17 less than four times x, and GI is 45 less than six times x, find the measure of ( GH ).