Final answer:
Triangle APOR, with angles in the ratio of 2:3:5, is a right triangle. The correct answer is 4) right.
Step-by-step explanation:
To determine the type of triangle APOR, we need to use the angle ratios given. The ratios of the angles in triangle PQR are 2:3:5. Let's assign values to these ratios. For example, if we let the smallest angle be 2x, the second angle would be 3x, and the largest angle would be 5x. Since the sum of the angles in a triangle is always 180 degrees, we can write the equation: 2x + 3x + 5x = 180.
Simplifying this equation, we get 10x = 180. Dividing both sides by 10, we find that x = 18. Now we can find the measures of the angles in triangle PQR by substituting x back into the ratios. The smallest angle is 2x = 2(18) = 36 degrees. The second angle is 3x = 3(18) = 54 degrees. The largest angle is 5x = 5(18) = 90 degrees.
Based on the angle measures, triangle APOR is a right triangle. Therefore, the correct answer is 4) right.