For a triangle, the ratio of all internal angles is A: B: C=2: 14: 20. Find the measure of each angle, if a triangle contains a total of 180 degrees.

Step 1 ：Given a triangle with the ratio of all internal angles as A: B: C=2: 14: 20. We know that a triangle contains a total of 180 degrees.

Step 2 ：First, we calculate the sum of the ratios, which is 2 + 14 + 20 = 36.

Step 3 ：Each ratio represents a fraction of the total 180 degrees. So, the measure of each angle can be found by multiplying the ratio for that angle by the fraction of the total degrees that the sum of the ratios represents.

Step 4 ：Using this method, we find that the measure of angle A is \(\frac{2}{36} * 180 = 10.0^\circ\)

Step 5 ：The measure of angle B is \(\frac{14}{36} * 180 = 70.0^\circ\)

Step 6 ：The measure of angle C is \(\frac{20}{36} * 180 = 100.0^\circ\)

Step 7 ：Final Answer: The measure of each angle is \(\boxed{A: 10.0^\circ, B: 70.0^\circ, C: 100.0^\circ}\)