Question

У треугольников MNK и MTK общая сторона – MK, MN = MT, NK = TK, ∠NKM = 116°. Чему равен ∠NKT ?​

Answer 1

Ответ:

Треугольник MNK= Треугольнику MTK

Соответственно угол NKM=Углу TKM= 116’

Угол NKT= угол NKM +Угол TKM = 116+116= 232’

Объяснение:

Answer 2

I can answer your question in detail. The triangles MNK and MTK have a common side - MK, MN = MT, NK = TK, ∠NKM = 116°. To find the value of ∠NKT, we can use the following steps:

- Since MN = MT and NK = TK, the triangles MNK and MTK are isosceles. - In an isosceles triangle, the angles opposite to the equal sides are also equal. Therefore, ∠MKN = ∠MTK and ∠NKM = ∠TKM. - Since ∠NKM = 116°, we can conclude that ∠TKM = 116° as well. - The sum of the angles in a triangle is 180°. Therefore, we can find the value of ∠MKT by subtracting the values of ∠TKM and ∠MTK from 180°. We get:

$$\begin{aligned} \angle MKT &= 180^\circ - \angle TKM - \angle MTK \\ &= 180^\circ - 116^\circ - \angle MTK \\ &= 64^\circ - \angle MTK \end{aligned}$$

- Since ∠MKT and ∠NKT are supplementary angles, their sum is 180°. Therefore, we can find the value of ∠NKT by subtracting the value of ∠MKT from 180°. We get:

$$\begin{aligned} \angle NKT &= 180^\circ - \angle MKT \\ &= 180^\circ - (64^\circ - \angle MTK) \\ &= 116^\circ + \angle MTK \end{aligned}$$

- To find the value of ∠MTK, we can use the sine rule for the triangle MTK. The sine rule states that for any triangle ABC, the ratio of the length of a side to the sine of the opposite angle is constant. That is:

$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$

- Applying the sine rule to the triangle MTK, we get:

$$\frac{MK}{\sin \angle MTK} = \frac{MT}{\sin \angle MKT} = \frac{TK}{\sin \angle TKM}$$

- Since MK = TK and ∠TKM = 116°, we can simplify the equation as follows:

$$\frac{1}{\sin \angle MTK} = \frac{1}{\sin \angle MKT} = \frac{1}{\sin 116^\circ}$$

- Solving for ∠MTK, we get:

$$\sin \angle MTK = \sin \angle MKT = \sin 116^\circ$$

- Taking the inverse sine of both sides, we get:

$$\angle MTK = \angle MKT = \sin^{-1}(\sin 116^\circ)$$

- Using a calculator, we can find the approximate value of ∠MTK as follows:

$$\angle MTK \approx 64^\circ$$

- Substituting this value into the expression for ∠NKT, we get:

$$\angle NKT \approx 116^\circ + 64^\circ = 180^\circ$$

- Therefore, the value of ∠NKT is 180°.

I hope this answer helps you understand the problem.