Question

Биссектрисы углов A и B треугольника ABC пересикаются в точке M.Найдите угол C , если угол AMB =145.

Answer 1

Ответ:

180-145=35см вот ответ такой ответ так как это свойства многоугольника

Answer 2

Given Information:

We have a triangle ABC where the bisectors of angles A and B intersect at point M. It is also given that angle AMB is equal to 145 degrees.

To Find:

We need to find the measure of angle C.

Solution:

In a triangle, the angle bisector of an angle divides the opposite side into two segments that are proportional to the adjacent sides of the triangle. This property is known as the Angle Bisector Theorem.

Let's apply the Angle Bisector Theorem to triangle ABC. The bisector of angle A divides side BC into two segments, let's call them BD and CD, where BD/CD = AB/AC.

Similarly, the bisector of angle B divides side AC into two segments, let's call them AE and CE, where AE/CE = AB/BC.

Now, let's denote the measure of angle BAC as x. According to the Angle Bisector Theorem, we have:

BD/CD = AB/AC AE/CE = AB/BC

Since we know that angle AMB is equal to 145 degrees, we can find the measure of angle BMA by subtracting 145 degrees from 180 degrees:

angle BMA = 180 degrees - angle AMB = 180 degrees - 145 degrees = 35 degrees

Now, let's use the fact that the angles in a triangle add up to 180 degrees. The sum of angles BMA and CMB must be equal to angle BMC:

angle BMA + angle CMB = angle BMC

Substituting the known values:

35 degrees + angle CMB = angle BMC

We also know that angle CMB is equal to angle BAC (since they are vertical angles). Therefore:

35 degrees + angle BAC = angle BMC

Now, let's consider triangle BMC. The sum of its angles must be equal to 180 degrees:

angle BMC + angle MBC + angle BAC = 180 degrees

Substituting the known values:

(35 degrees + angle BAC) + angle MBC + angle BAC = 180 degrees

Simplifying the equation:

2 * angle BAC + angle MBC = 180 degrees - 35 degrees 2 * angle BAC + angle MBC = 145 degrees

Now, let's consider triangle ABC. The sum of its angles must be equal to 180 degrees:

angle BAC + angle ABC + angle BCA = 180 degrees

Substituting the known values:

angle BAC + angle ABC + (180 degrees - angle BAC - angle ABC) = 180 degrees

Simplifying the equation:

angle BAC + angle ABC + 180 degrees - angle BAC - angle ABC = 180 degrees 180 degrees = 180 degrees

This means that the equation is always true, regardless of the values of angle BAC and angle ABC. Therefore, we cannot determine the exact measure of angle C without additional information.

Hence, the measure of angle C cannot be determined with the given information.