Question

В треугольнике MNK ND-биссектриса.Найдите градусную меру NDK.Угол M 52°,Угол K 30°.Помогите пожалуйстааа

Answer 1

Сумма углов треугольника = 180 градусов => угол MNK = 180 - ( угол М + угол К) = 180 - (52 +30) = 98 градусов.
ND - биссектриса => угол MND = углу DNK. Тогда угол DNK = 98 : 2 = 46 градусов.
Сумма углов треугольника = 180 градусов => угол NDK = 180 - (46 + 30) = 104 градуса.

Answer 2

Сумма углов в треугольнике - 180.
180 = M + K + N 
180 = 52 + 30 + N
N = 180 - 82 = 98
Биссектриса делит угол пополам.
Угол KND = 98/2 = 49
Сумма углов в треугольнике - 180.
180 = KND + K + NDK
180 = 49 + 30 + NDK
NDK = 180 - 79 = 101

Answer 3

Problem Analysis

We are given a triangle MNK, where ND is the angle bisector of angle MNK. We need to find the measure of angle NDK, given that angle M is 52° and angle K is 30°.

Solution

To find the measure of angle NDK, we can use the angle bisector theorem. According to this theorem, the angle bisector of an angle in a triangle divides the opposite side into two segments that are proportional to the lengths of the other two sides.

Let's denote the length of segment ND as x and the length of segment DK as y. Then, we can set up the following proportion:

ND / NK = MD / MK

Since ND is the angle bisector, we know that MD = MK. Therefore, the proportion becomes:

ND / NK = MD / MK = MK / MK = 1

Simplifying the proportion, we have:

ND = NK

This means that segment ND is equal in length to segment NK.

Now, let's consider triangle NDK. We know that the sum of the angles in a triangle is 180°. Therefore, we can set up the following equation:

NDK + NDK + K = 180°

Substituting the given values, we have:

NDK + NDK + 30° = 180°

Combining like terms, we get:

2NDK + 30° = 180°

Simplifying the equation, we have:

2NDK = 150°

Dividing both sides by 2, we find:

NDK = 75°

Therefore, the measure of angle NDK is 75°.

Conclusion

In triangle MNK, with ND as the angle bisector, the measure of angle NDK is 75°.