The possible values of angle K in triangle KLM, to the nearest 10th of a degree, are 19.0° and 341.0°.
The notation "ZM-161°" doesn't make sense in the context of finding the angle K in triangle KLM. It could be interpreted as:
"ZM = -161°": This would imply ZM is a negative length, which is impossible.
"∠ZM = -161°": This would also be impossible as angles cannot be negative.
"∠M = 161°": This is the most likely interpretation, where angle M is given as 161 degrees.
Assuming the intended meaning is "∠M = 161°" and you want to find all possible values of angle K, here's how you can proceed:
Use the Law of Sines: This law states that the ratio of the sides of a triangle is equal to the ratio of the sines of their opposite angles.
In this case, you can write:
k / sin(K) = m / sin(M)
Substitute the known values: Replace k with 94, m with 79, and M with 161°:
94 / sin(K) = 79 / sin(161°)
Solve for K: Solve the equation for K.
This will involve taking the arcsine (sin^-1) of both sides and rounding to the nearest 10th of a degree.
Using a calculator, you'll get two possible values for K:
K ≈ 19.0°
K ≈ 341.0°
Therefore, the possible values of angle K in triangle KLM, to the nearest 10th of a degree, are 19.0° and 341.0°.