Question

Внутри угла АОВ проведен луч ОС,а внутри угла СОВ -луч ОЕ.градусная мера угла АОС равна 54,3. угол СОЕ на 17,8 меньше угла АОС и на 26,9 меньше угла ВОЕ. найдите угол АОВ

Answer 1

∠СОЕ = ∠АОС - 17,8 = 54,3 - 17,8 = 36,5°
∠ВОЕ = ∠СОЕ + 26,9 = 36,5 + 26,9 = 63,4°
∠АОВ = ∠АОС + ∠СОЕ + ∠ВОЕ = 54,3+ 36,5 + 63,4 = 154,2°

Answer 2

Кут AOC=54.3
кут COE=54.3-17.8=36.5
кут BOE=29.9-17.8+36.5=48.6
кут AOB=54.3+36.5+48.6=129.4

Answer 3

Given Information

The given information states that inside angle AOB, ray OS is drawn, and inside angle SOB, ray OE is drawn. The measure of angle AOS is 54.3 degrees, and the angle SOE is 17.8 degrees less than angle AOS and 26.9 degrees less than angle BOE. We need to find the measure of angle AOB.

Solution

To find the measure of angle AOB, we can use the information provided about the angles AOS, SOE, and BOE.

Given: - Angle AOS = 54.3 degrees - Angle SOE = 17.8 degrees less than angle AOS - Angle SOE = 26.9 degrees less than angle BOE

We can use the information to find the measure of angle AOB.

First, we can find the measure of angle SOE: - Angle SOE = Angle AOS - 17.8 degrees - Angle SOE = 54.3 degrees - 17.8 degrees - Angle SOE = 36.5 degrees

Next, we can find the measure of angle BOE: - Angle SOE = Angle BOE - 26.9 degrees - 36.5 degrees = Angle BOE - 26.9 degrees - Angle BOE = 36.5 degrees + 26.9 degrees - Angle BOE = 63.4 degrees

Finally, we can find the measure of angle AOB: - Angle AOB = Angle AOS + Angle BOE - Angle AOB = 54.3 degrees + 63.4 degrees - Angle AOB = 117.7 degrees

Therefore, the measure of angle AOB is 117.7 degrees.