Question

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Answer 1

60°

Решение задания прилагаю

Answer 2

Ответ:

$60^{\circ}.$

Пошаговое объяснение:

$\angle BAM=\angle KAB+\angle KAM;$

$\angle KAM=(180^{\circ}-\angle AMK):2;$

$\angle AMK=180^{\circ}-\angle AMC \Rightarrow \angle KAM=(180^{\circ}-(180^{\circ}-\angle AMC)):2=$

$=\angle AMC:2;$

$\angle KAM=\angle AMC:2 \Rightarrow \angle AMC=2 \cdot \angle KAM;$

$\angle CAM=180^{\circ}-\angle AMC-\angle C=180^{\circ}-2 \cdot \angle KAM-\angle C;$

$\angle KAB=180^{\circ}-\angle AKB-\angle B=180^{\circ}-(180^{\circ}-\angle KAM)-\angle B=\angle KAM-\angle B;$

$\angle CAM=\angle KAB \Rightarrow 180^{\circ}-2 \cdot \angle KAM-\angle C=\angle KAM-\angle B;$

$2 \cdot \angle KAM+\angle KAM+\angle C-\angle B=180^{\circ};$

$\angle C=(180^{\circ}-\angle B):2;$

$3\angle KAM+(180^{\circ}-\angle B):2-\angle B=180^{\circ} \quad | \quad \cdot 2$

$6\angle KAM+180^{\circ}-3\angle B=360^{\circ};$

$6\angle KAM-3\angle B=360^{\circ}-180^{\circ};$

$6\angle KAM-3\angle B=180^{\circ};$

$\angle B=2\angle KAM-60^{\circ};$

$\angle KAB=\angle KAM-(2\angle KAM -60^{\circ})=60^{\circ}-\angle KAM;$

$\angle BAM=\angle KAB+\angle KAM;$

$\angle BAM=60^{\circ}-\angle KAM+\angle KAM=60^{\circ};$