Final answer:
The measure of the greatest angle of a triangle can be found by setting up and solving an equation based on the angles' ratios.
Step-by-step explanation:
In a triangle, the sum of the three angles is always 180 degrees. Let's assume that the measures of the angles are 1x, 2x, and 3x. Since the ratio of the angles is 1:2:3, we can write the equation 1x + 2x + 3x = 180. Simplifying this equation gives us 6x = 180. Dividing both sides by 6, we find that x = 30.
The measure of the greatest angle, which is 3x, is therefore 3 * 30 = 90 degrees.