Question

Решите задачу.Meдиана AM треугольника АВС продолжена за сторону ВС на отрезок МК, равный АМ, и точка К соединена с точкой С. Найдите угол СКМ (в градусах), если ∠АСМ=65°∠ВАМ=28° Чертежа не дано.

Answer 1

.1. Полученный четырехугольник - параллелограмм, Т.к. ВМ=МС ( АМ- биссектриса)                                                                                     АМ=МК9 по построению,А четырехугольник у которого диагонали точкой пересечения делятся пополам - параллелограм 2) Т.к АВКС-параллелограмм, то АВ||KC, AC||BK3) Углы СКМ и ВАМ- накрестлежащие при АВ||KC и секущей АК, значит они равны и равны 28гр )) вот ка

Answer 2

Problem Analysis

We are given a triangle ABC, and the median AM is extended beyond side BC to point K such that MK is equal to AM. Point K is then connected to point C. We need to find the angle SKM, given that angle ASM is 65° and angle BAM is 28°.

Solution

To find the angle SKM, we can use the fact that the medians of a triangle divide each other into segments of equal length. In other words, the length of BK is equal to twice the length of KC.

Let's denote the length of AM as x. Since MK is equal to AM, the length of MK is also x. Therefore, the length of BK is 2x, and the length of KC is x.

Now, let's consider triangle BKC. We know that the sum of the angles in a triangle is 180°. We can use this fact to find angle BKC.

Let angle BKC be denoted as y. Since angle BAM is 28°, angle BAC is 2 * 28° = 56° (because the median divides the angle into two equal parts). Similarly, angle BCA is 56°.

Using the fact that the sum of the angles in a triangle is 180°, we can write the following equation:

y + 56° + 56° = 180°

Simplifying the equation, we have:

y + 112° = 180°

Subtracting 112° from both sides, we get:

y = 180° - 112°

y = 68°

Therefore, angle BKC is 68°.

Now, let's consider triangle SKM. We know that angle ASM is 65°. Since angle ASM and angle BKC are corresponding angles (formed by parallel lines MK and BC), they are equal. Therefore, angle SKM is also 65°.

To find angle CKM, we can subtract angle SKM from angle BKC:

angle CKM = angle BKC - angle SKM = 68° - 65° = 3°.

Therefore, the angle CKM is 3°.

Answer

The angle CKM is 3°.