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's denote the smallest angle as \( x \). According to the problem, the second angle can be expressed as \( x + 24 \) degrees, and the third angle as \( 4x \) degrees. Now, we know that the angles in a triangle sum up to 180 degrees. Therefore, we can set up the equation: \[ x + (x + 24) + 4x = 180 \] Combining like terms, we get: \[ 6x + 24 = 180 \] Next, we can subtract 24 from both sides: \[ 6x = 156 \] Now, we divide by 6: \[ x = 26 \] Thus, the measure of the smallest angle is 26 degrees. The second angle would be 50 degrees, and the third angle would be 104 degrees. In summary, the smallest angle of the triangle is 26 degrees.