In a triangle, the measure of the first angle is 24 degrees more than the measure of the second angle. The measure of the third angle is four times the measure of the second angle. If the total number of degrees in a triangle is 180, what is the measure of the largest angle?

Let the second angle be x degrees. Then the first angle is x + 24 and the third is 4x, so x + (x + 24) + 4x = 180; solving gives 6x = 156 and x = 26. The third angle is 4 × 26 = 104 degrees, the largest angle, so the answer is 104 degrees.

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