Final answer:
By assigning a variable to the common factor in the ratio of angles and solving for it using the sum of angles at a point, we find that the angles measure 72 degrees, 108 degrees, and 180 degrees.
Step-by-step explanation:
When solving problems involving the measures of angles at a point, we often use the concept that the sum of these angles is 360 degrees, especially when the angles form a complete revolution around a point. If the measures of three angles at a point are in the ratio of 2:3:5, we let x be the common factor to each part of the ratio.
The measure of the first angle is 2x, the second angle is 3x, and the third angle is 5x. Since the sum of angles at a point is 360 degrees, we write the equation:
2x + 3x + 5x = 360
Combining like terms gives us:
10x = 360
Dividing both sides by 10 to solve for x gives:
x = 36
Now, to find each angle, we multiply x by the respective ratio:
First Angle = 2x = 2 * 36 = 72 degrees
Second Angle = 3x = 3 * 36 = 108 degrees
Third Angle = 5x = 5 * 36 = 180 degrees