Final answer:
To find the possible values of angle 1 in triangle JKLI, subtract the given angle K from 180 to get the sum of the other two angles. Then, use trigonometry and the law of cosines to solve for angle 2.
Step-by-step explanation:
To find the possible values of angle 1 in triangle JKLI, we can use the fact that the sum of the angles in a triangle is always 180 degrees. Since angle K is given as 10 degrees, we can subtract that from 180 degrees to find the sum of the other two angles in triangle JKLI.
So, angle 1 + angle 2 = 180 - angle K = 170 degrees.
Given that the length of side KI is 53 inches and the length of side K is 17 inches, we can use trigonometry to determine the measure of angle 2. Applying the law of cosines, we have:
cos(angle 2) = (side KI^2 + side K^2 - side IK^2) / (2 * side KI * side K) = (53^2 + 17^2 - 2 * 53 * 17 * cos(angle 2)) / (2 * 53 * 17)
Solving the equation above we find the possible values of angle 2 to the nearest degree.