Bunuel
Are the two triangles similar?
(1) The ratio of the measures of the angles in one triangle is 2 : 3 : 4.
(2) The ratio of the measures of the angles in the other triangle is 4 : 3 : 2.
Asked: Are the two triangles similar?
(1) The ratio of the measures of the angles in one triangle is 2 : 3 : 4.
Angles = {2x,3x,4x}
2x + 3x + 4x = 9x = 180
x = 20
Angles = {40,60,80}
Since angles of another triangle are unknown
NOT SUFFICIENT
(2) The ratio of the measures of the angles in the other triangle is 4 : 3 : 2.
Angles = {4x,3x,2x}
4x + 3x + 2x = 9x = 180
x = 20
Angles = {80,60,40}
Since angles of another triangle are unknown
NOT SUFFICIENT
Combining (1) & (2)
(1) The ratio of the measures of the angles in one triangle is 2 : 3 : 4.
Angles = {2x,3x,4x}
2x + 3x + 4x = 9x = 180
x = 20
Angles = {40,60,80}
(2) The ratio of the measures of the angles in the other triangle is 4 : 3 : 2.
Angles = {4x,3x,2x}
4x + 3x + 2x = 9x = 180
x = 20
Angles = {80,60,40}
Since all angles of the 2 triangles are same
Triangles are similar
SUFFICIENT
IMO C