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The heights of a triangle ABC meet at a point K.AB=CK.Find the angle of C.​

Sagot :

Answer:

45°

Step-by-step explanation:

AD⊥BC, BE⊥AC, CF⊥AB           AB = CK

∠1 + ∠2 = 90°        ∠5 + ∠2 = 90°              ∴ ∠1 = ∠5

∠5 + ∠4 = 90°                                            ∴ ∠4 = ∠2

AB = CK

ΔABD ≅ ΔCKD  (ASA)

AD = CD       ∴ΔADC is an isosceles triangle

∠C = ∠CAD = 45°       (∠C + ∠CAD = 90°)

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