Given TWO SETS of congruent angles,
what is the probability of selecting two consecutive angles that are congruent?
To find the probability of selecting two consecutive angles that are congruent from two sets of congruent angles, we need to consider the total number of possible pairs and the number of favorable pairs.
Let's assume we have two sets, Set A and Set B, each containing n congruent angles. Since the angles are congruent, it means that all the angles in Set A are equal in measure, and all the angles in Set B are also equal in measure.
To determine the probability, we need to calculate the number of favorable pairs and the total number of possible pairs.
Step 1: Calculate the total number of possible pairs:
For Set A, there are n angles, and we can choose any of these angles as the first angle. For the second angle to be a consecutive angle, there is only one angle that would fulfill this condition (since all angles in Set A are equal). Therefore, for Set A, we have n possible choices for the first angle and 1 possible choice for the second angle.
Similarly, for Set B, there are also n possible choices for the first angle and 1 possible choice for the second angle.
Thus, the total number of possible pairs is n * 1 = n.
Step 2: Calculate the number of favorable pairs:
To form a favorable pair, the first angle can be chosen from Set A or Set B, and the second angle must be chosen from the same set.
The number of favorable pairs would be:
1. If the first angle is chosen from Set A, there are n possible choices, and the second angle must also be chosen from Set A, giving us n * 1 = n favorable pairs.
2. If the first angle is chosen from Set B, the same logic applies, and we also get n favorable pairs.
Hence, the total number of favorable pairs is n + n = 2n.
Now, to find the probability, we divide the number of favorable pairs by the total number of possible pairs:
Probability = Number of Favorable Pairs / Total Number of Possible Pairs
= 2n / n
= 2
Therefore, the probability of selecting two consecutive angles that are congruent from two sets of congruent angles is 2 or 200% (assuming the number of angles in each set is the same).