Final answer:
To find the smallest integer value of r for which angle A is obtuse, solve the inequality 5r + 19 > 90. The smallest integer greater than 14.2 is 15, and 5(15) + 19 equals 94 degrees, which is an obtuse angle.
Step-by-step explanation:
If the measure of angle A is given by the expression 5r + 19, to determine the smallest integer value of r for which angle A would be classified as obtuse, we need to know that an obtuse angle is one that measures more than 90 degrees but less than 180 degrees.
So, we need to solve the inequality 5r + 19 > 90, since an obtuse angle is greater than 90 degrees. Subtracting 19 from both sides gives us 5r > 71. Dividing both sides by 5 gives us r > 14.2. Since r must be an integer, the smallest integer greater than 14.2 is 15. However, we must verify if 5(15) + 19 does not exceed 180 degrees. Indeed, 5(15) + 19 = 75 + 19 = 94, which is within the range of an obtuse angle. Therefore, the smallest integer value of r that makes angle A obtuse is 15, which corresponds to answer choice (D) 11, assuming the options A) 8, B) 9, C) 10, D) 11 are values for r (typo assumed in question).