Two angles of a pentagon are in the ratio 2:3. The others are 60o each. Calculate the smaller of the two angles

Answer Details

Let's call the two angles that are in the ratio 2:3 as "2x" and "3x". The sum of the interior angles of a pentagon is given by the formula (5-2) x 180 degrees = 540 degrees. Since the other three angles are all 60 degrees each, we can find the sum of those angles by multiplying 60 by 3, which gives us 180 degrees. Now we can set up an equation to solve for the unknown angle, which is 2x + 3x. 2x + 3x + 180 = 540 Simplifying this equation, we get: 5x + 180 = 540 Subtracting 180 from both sides, we get: 5x = 360 Dividing both sides by 5, we get: x = 72 So the smaller angle, which is 2x, is equal to 2 times 72, which is 144 degrees. Therefore, the correct answer is 144 degrees.