Question

Дано: угол ВОС= 80 градусов; ОА луч. Угол АОС: угол АОВ= 1:3.Найти угол АОС;угол АОВ

Answer 1

AOB=80-AOC
3AOC=80-AOC
2AOC=80
AOC=40
AOB=80/40
AOB=40

Answer 2

Given Information:

- Angle VOS = 80 degrees - OA is a ray - Angle AOS: Angle AOV = 1:3

Finding Angle AOS and Angle AOV:

To find the measures of Angle AOS and Angle AOV, we need to use the given information and apply some geometric principles.

Let's start with Angle AOS. We know that Angle AOS + Angle AOV = Angle VOS. Since Angle AOV is 1/3 of Angle AOS, we can express this relationship as:

Angle AOS + (1/3) * Angle AOS = 80 degrees

Simplifying the equation, we have:

(4/3) * Angle AOS = 80 degrees

To solve for Angle AOS, we can multiply both sides of the equation by (3/4):

Angle AOS = (3/4) * 80 degrees

Calculating the value, we find:

Angle AOS = 60 degrees

Now, let's find Angle AOV. We know that Angle AOV is 1/3 of Angle AOS. Using the value we found for Angle AOS, we can calculate Angle AOV as:

Angle AOV = (1/3) * Angle AOS

Substituting the value of Angle AOS, we have:

Angle AOV = (1/3) * 60 degrees

Calculating the value, we find:

Angle AOV = 20 degrees

Therefore, the measures of Angle AOS and Angle AOV are 60 degrees and 20 degrees, respectively.

Note: The search results did not provide direct snippets for this specific question. The solution is derived using geometric principles and calculations.