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.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 38°.
The smallest angle (x) is 42° less than the greatest angle (z):
⇒ x = z - 42
⇒ z = x + 42°
The middle angle (y) is 24° more than the smallest angle (x):
⇒ y = x + 24
The sum of the angles of a triangle is always 180°:
⇒ x + y + z = 180°
⇒ x + x + 24 + x + 42° = 180°
⇒ x = 114/3 = 38°