The measures of the three angles of a triangle are such that the smallest angle measures 42° less than the greatest angle, while the measure of the remaining angle is 24° more than the measure of the smallest angle. Find the measure of the smallest angle of the triangle.

Correct option is C

Given:
The smallest angle is 42° less than that of the largest angle while the measure of the remaining angle is 24° more than the measure of the smallest angle.
Concept used:
All three angles of a triangle sum up to 180°.
Solution:
Let largest angle be x°
Smallest angle = (x- 42)°
Remaining angle =(x- 42+24)°= (x- 18)°
Now, we have
x° +(x- 42)°+ (x- 18)°= 180°
=> 3x - 60°= 180°
=> 3x = 240°
=> x = 80°
∴ smallest angle = 80° - 42°=38°