Question

What is the ratio of one interior angle of an equilateral triangle to one interior angle of a square? Express your answer as a common fraction.

Answer 1

recalling that a triangle has a sum of interior angles to be 180°, for an equilateral triangle that also means an equiangular triangle, so all angles are equal, that means each angle is 60°.

a square has each interior angle at 90°.

what's their ratio?

$\bf \cfrac{triangle}{square}\qquad \qquad \cfrac{60}{90}\implies \cfrac{6}{9}\implies \cfrac{2}{3}$