ZQPK-3,5 ZQPM ZM : ZQ-3:4 ZM, ZQ, ZQPM - ?

Пусть $$\angle M = 3x, \angle Q = 4x$$. По теореме о сумме углов треугольника:

$$\angle M + \angle Q + \angle QPM = 180^{\circ}$$.

$$3x + 4x + \angle QPM = 180^{\circ}$$.

$$7x + \angle QPM = 180^{\circ}$$.

$$\angle QPM = 180^{\circ} - 7x$$.

$$\angle QPK = 3,5 \angle QPM$$.

Углы $$\angle QPK$$ и $$\angle QPM$$ - смежные, поэтому их сумма равна $$180^{\circ}$$.

$$\angle QPK + \angle QPM = 180^{\circ}$$.

$$3,5 \angle QPM + \angle QPM = 180^{\circ}$$.

$$4,5 \angle QPM = 180^{\circ}$$.

$$\angle QPM = \frac{180^{\circ}}{4,5} = 40^{\circ}$$.

$$7x = 180^{\circ} - \angle QPM = 180^{\circ} - 40^{\circ} = 140^{\circ}$$.

$$x = \frac{140^{\circ}}{7} = 20^{\circ}$$.

Тогда,

• $$\angle M = 3 \cdot 20^{\circ} = 60^{\circ}$$
• $$\angle Q = 4 \cdot 20^{\circ} = 80^{\circ}$$
• $$\angle QPM = 40^{\circ}$$

Ответ: $$\angle M = 60^{\circ}$$, $$\angle Q = 80^{\circ}$$, $$\angle QPM = 40^{\circ}$$