ZSTM-2ZS ZS, STR-? 70°

Пусть $$\angle S = x$$, тогда $$\angle STM = 2x$$. Сумма углов треугольника равна $$180^{\circ}$$.

$$\angle S + \angle STM + \angle R = 180^{\circ}$$.

$$x + 2x + 70^{\circ} = 180^{\circ}$$.

$$3x = 180^{\circ} - 70^{\circ} = 110^{\circ}$$.

$$x = \frac{110^{\circ}}{3} = 36\frac{2}{3}^{\circ}$$.

$$\angle S = 36\frac{2}{3}^{\circ}$$.

$$\angle STM = 2 \cdot 36\frac{2}{3}^{\circ} = 73\frac{1}{3}^{\circ}$$.

$$\angle STR$$ и $$\angle STM$$ - смежные, поэтому их сумма равна $$180^{\circ}$$.

$$\angle STR = 180^{\circ} - \angle STM = 180^{\circ} - 73\frac{1}{3}^{\circ} = 106\frac{2}{3}^{\circ}$$.

Ответ: $$\angle S = 36\frac{2}{3}^{\circ}$$, $$\angle STR = 106\frac{2}{3}^{\circ}$$