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do question nine. note that this is simultaneous equations and show full working out. hint, the answer is x equal 39 degrees and y equal 52 degrees and angle k is 90 degrees.

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°

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step-by-step explanation: