Answer:
To find the measures of each angle, we first need to determine the total measure of all three angles in the triangle. Since the sum of the measures of the angles in any triangle is 180 degrees, we can find the total measure of all three angles by multiplying the ratio 2:5:3 by 180.
We can find the total measure of all three angles by using the rule of three.
2/5+5/3+3/2 = 180/x
Solving for x:
x = 1802532/ (2+5+3) = 180*60/10 = 1080
So, the total measure of all three angles is 1080 degrees.
Then, we can find the measure of each angle by multiplying the fraction of the ratio that represents that angle by the total measure of all three angles.
The measure of the first angle is: 2/10 * 1080 = 216 degrees
The measure of the second angle is: 5/10 * 1080 = 540 degrees
The measure of the third angle is: 3/10 * 1080 = 324 degrees