Question

Угол АОВ равен 87 градусов. Внутри данного угла проведен луч ОС. Найдите градусную меру угла АОС если ВОС=52 ГРАДУСОВ .НАЧЕРТИТЕ В ТЕТРАДИ РИСУНОК ПОусловию задачи....

Answer 1

Ответ смотри во вложении

Answer 2

Угол АОВ= угол АОС+ВОС=87 градусов;
АОС=87-52=35 градусов.

Answer 3

Task Analysis

The problem involves finding the measure of angle AOS given that the measure of angle AOV is 87 degrees and the measure of angle VOS is 52 degrees.

Solution

To find the measure of angle AOS, we can use the fact that the sum of the measures of angles around a point is 360 degrees. We can calculate the measure of angle AOS using the given information.

Given: - Measure of angle AOV = 87 degrees - Measure of angle VOS = 52 degrees

Calculation

We can calculate the measure of angle AOS using the following steps: 1. Calculate the measure of angle AOV. 2. Calculate the measure of angle VOA. 3. Use the fact that the sum of the measures of angles around a point is 360 degrees to find the measure of angle AOS.

Step-by-Step Calculation

1. Measure of angle AOV = 87 degrees 2. Measure of angle VOS = 52 degrees 3. Measure of angle AOV + Measure of angle VOA + Measure of angle VOS = 360 degrees - Measure of angle VOA = 360 - Measure of angle AOV - Measure of angle VOS - Measure of angle VOA = 360 - 87 - 52 - Measure of angle VOA = 221 degrees 4. Measure of angle AOS = Measure of angle AOV + Measure of angle VOA - Measure of angle AOS = 87 + 221 - Measure of angle AOS = 308 degrees

Answer

The measure of angle AOS is 308 degrees.

Sketch

I'm unable to physically draw the diagram, but you can represent the angles on a piece of paper as follows: - Angle AOV = 87 degrees - Angle VOS = 52 degrees - Angle AOS = 308 degrees

This should help visualize the angles as per the given conditions.