Question

The measure of one acute angle in a right triangle is fourteen times the measure of the other acute angle. The measure of the larger acute angle is equal to____ degrees. (Hint: Let the acute angles equal x and 14x)

a) 60 degrees
b) 75 degrees
c) 80 degrees
d) 85 degrees

Answer 1

The measure of the larger acute angle in a right triangle, where one angle is fourteen times the other, is determined to be 84 degrees by using the fact that the sum of angles in a triangle is 180 degrees and solving for x in the equation x + 14x = 90.

Step-by-step explanation:

The measure of one acute angle in a right triangle is fourteen times the measure of the other acute angle. To find the measure of the larger acute angle, we let the smaller angle be x degrees and the larger angle be 14x degrees. Since the sum of angles in any triangle is 180 degrees and one angle is already 90 degrees (because it is a right triangle), the other two angles must sum to 90 degrees. Therefore, we have the equation:

x + 14x = 90

15x = 90

x = 90 / 15 = 6

The larger angle is 14x, which is 14 * 6 = 84 degrees. This means that the measure of the larger acute angle is 84 degrees, which is closest to option (d) 85 degrees.