Question

СРОЧНО!!! Контрольная работа Начальные геометрические сведения РЕШИТЕ ПОЖАЛУЙСТА ДАМ 40 баллов.1.Сумма вертикальных углов MOE,POK образованных при пересечении прямых MK иPE Равна 198грудусамнайдите угол MOP2.С помощью транспортира начертите угол равный 56градусам и проведите биссектрису смежного угла 3.Из точки B проведены три луча BM,BN,BK найдите угол NBK если угол MBN=84градусам, а угол MBK=22 градусам​

Answer 1

Відповідь:

Пояснення:

1)Вертикальные углы равны, а значит ∠ MOE= ∠POK, по-этому градусная мера каждого угла будет 198/2=99°

∠ МОР ∠ МОЕ смежные, следовательно сумма их равна 180°. Отсюда ∠МОР=180-99=81 град

рисунок ниже

Ответ: 81°

2)∠BOC = 56°

∠BOC + ∠AOC = 180° - смежные углы

∠AOC = 180° - 56° = 124°

OM - биссектриса ∠AOC

∠AOM = ∠MOC = ∠AOC : 2 = 124° : 2 = 62° (рис 2 транспортир)

3)Есть больший угол MBN = 84 градусам. Внутри него проведен луч, который делит его на два  угла MBK = 22 градусам и NBK который нужно найти. От большего угла отнимаем его известную часть и находим неизвестный угол.

NBK = MBN - MBK = 84-22 = 62 градуса.

Answer 2

1. Finding the angle MOP: To find the angle MOP, we need to use the fact that the sum of vertical angles is equal to 180 degrees. In this case, the vertical angles are MOE and POK, which are formed by the intersection of the lines MK and PE. Given that the sum of these angles is 198 degrees, we can set up the equation:

MOE + POK = 198 degrees

Since vertical angles are equal, we can rewrite the equation as:

2 * MOE = 198 degrees

Solving for MOE, we get:

MOE = 198 degrees / 2 = 99 degrees

Therefore, the angle MOP is 99 degrees.

2. Drawing an angle of 56 degrees and bisecting the adjacent angle: To draw an angle of 56 degrees, follow these steps: - Start by drawing a line segment. - Place the center of the protractor on one endpoint of the line segment. - Align the baseline of the protractor with the line segment. - Find the 56-degree mark on the protractor and mark a point on the line segment. - Draw a line from the endpoint through the marked point to create the desired angle.

To bisect the adjacent angle, follow these steps: - Place the center of the protractor on the vertex of the angle. - Align the baseline of the protractor with one of the arms of the angle. - Find the 28-degree mark on the protractor and mark a point on the other arm of the angle. - Draw a line from the vertex through the marked point to bisect the angle.

3. Finding the angle NBK: To find the angle NBK, we need to use the fact that the sum of the angles in a triangle is equal to 180 degrees. In this case, we have a triangle formed by the rays BM, BN, and BK. Given that the angle MBN is 84 degrees and the angle MBK is 22 degrees, we can set up the equation:

MBN + MBK + NBK = 180 degrees

Substituting the given values, we get:

84 degrees + 22 degrees + NBK = 180 degrees

Simplifying the equation, we find:

NBK = 180 degrees - 84 degrees - 22 degrees = 74 degrees

Therefore, the angle NBK is 74 degrees.

I hope this helps! Let me know if you have any further questions.