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.

The correct answer is 38°.

Step-by-step explanation:

Let the measures of the three angles of the triangle be represented as follows:
Let $s$ be the measure of the smallest angle.
Let $g$ be the measure of the greatest angle.
Let $m$ be the measure of the remaining (middle) angle.

From the problem statement, we are given two relationships:

1. The smallest angle measures 42° less than the greatest angle:
$s=g-42°$
This can also be rewritten to express $g$ in terms of $s$:
$g=s+42°$

2. The measure of the remaining angle is 24° more than the measure of the smallest angle:
$m=s+24°$

We know that the sum of the measures of the three interior angles of any triangle is always equal to 180°:
$s+m+g=180°$

Now, substitute the expressions for $g$ and $m$ in terms of $s$ into the angle sum equation:

$s+(s+24°)+(s+42°)=180°$

Combine the like terms:

$3s+66°=180°$

Subtract 66° from both sides of the equation:

$3s=180°-66°$

$3s=114°$

Divide by 3 to solve for $s$:

$s=\frac{114°}{3}$

$s=38°$

Thus, the measure of the smallest angle of the triangle is 38°.