Question

in an equilateral each angle has measure 60 ° true or false​

Answer 1

Answer:

Step-by-step explanation:

True - In equilateral Triangle each angle measures  60°.

Answer 2

GIVEN,

an equilateral

TO FIND,

prove that the angles of an equilateral triangle are 60° each.

SOLUTION,

Let △XYZ be an equilateral triangle.

Then,

since the three edges of an equilateral triangle are equal,

XY=YZ=ZX

Since angles polar to equal sides of a triangle are equal.

XY=YZ and YZ=XZ

hence,

⟹∠Z=∠X and ∠X=∠Y

so each angle is equal since each side is equal,

⟹∠X=∠Y=∠Z

But, ∠X+∠Y+∠Z=180°

area of a triangle is 180°

Therefore, 3∠X=180°

∠X=60°

Hence, ∠X=∠Y=∠Z=60°

THEREFORE EACH ANGLE OF AN EQUILATERAL TRIANGLE IS 60°