To find the measure of angle K in kite JKL-M, we start by recalling some properties of kites. A kite has two pairs of adjacent sides that are equal and one pair of opposite angles that are equal. In this case, we can use the fact that the sum of the angles in any quadrilateral is 360 degrees.
We know the measures of angles J, M, and L as given:
- Angle J = 78 degrees
- Angle M = 118 degrees
- Angle L = 46 degrees
Now, we can find the measure of angle K:
Sum of angles in quadrilateral = Angle J + Angle K + Angle L + Angle M = 360 degrees
Substituting the known angles into the equation:
78 + Angle K + 46 + 118 = 360
Combining the known angles:
242 + Angle K = 360
To isolate Angle K, we subtract 242 from both sides:
Angle K = 360 – 242
Angle K = 118 degrees
Thus, the measure of angle K in kite JKL-M is 118 degrees.