Answer:
see explanation
Step-by-step explanation:
Since KL = KM then the triangle is isosceles and the 2 base angles are congruent, that is
∠KLM = ∠KML, thus
y - 9 = x + 4 (add 9 from both sides )
y = x + 13 → (1)
The sum of the 3 angles in the triangle = 180°, thus
x + 4 + y - 9 + x + y + 3 = 180
2x + 2y - 2 = 180 ( add 2 to both sides )
2x + 2y = 182 → (2)
Substitute y = x + 13 into (2)
2x + 2(x + 13) = 182 ← distribute and simplify left side
2x + 2x + 26 = 182
4x + 26 = 182 ( subtract 26 from both sides )
4x = 156 ( divide both sides by 4 )
x = 39
Substitute x = 39 into (1)
y = 39 + 13 = 52
Hence
∠K = x + y + 3 = 39 + 52 + 3 = 94°
