The angles of a triangle add up to 180 degrees. The second angle is 24 degrees larger than the smallest angle. The third angle is 4 times as big as the smallest angle. Find the measure of the smallest angle (in degrees)

Let the smallest angle be denoted as \( x \) degrees. According to the problem: - The second angle is \( x + 24 \) degrees. - The third angle is \( 4x \) degrees. The sum of the angles in a triangle is 180 degrees, so we can set up the following equation: \[ x + (x + 24) + 4x = 180 \] Now, combine like terms: \[ x + x + 24 + 4x = 180 \] \[ 6x + 24 = 180 \] Next, subtract 24 from both sides: \[ 6x = 180 - 24 \] \[ 6x = 156 \] Now, divide both sides by 6 to solve for \( x \): \[ x = \frac{156}{6} = 26 \] Thus, the measure of the smallest angle is \( \boxed{26} \) degrees. To verify, we can calculate the other angles: - The second angle is \( 26 + 24 = 50 \) degrees. - The third angle is \( 4 \times 26 = 104 \) degrees. Now, check the sum: \[ 26 + 50 + 104 = 180 \] Since the angles add up to 180 degrees, our solution is confirmed. The smallest angle is indeed \( \boxed{26} \) degrees.