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Теория: Смежные углы

Задание

Дополните таблицу величин смежных углов.

 

Величина угла \(\displaystyle \alpha\)

Величина угла \(\displaystyle \beta\)

\(\displaystyle 40\degree \)

\(\displaystyle \degree \)

\(\displaystyle 90\degree \)

\(\displaystyle \degree \)

\(\displaystyle 133\degree \)

\(\displaystyle \degree \)

\(\displaystyle 28\degree 35'\)

\(\displaystyle \degree \)\(\displaystyle '\)

\(\displaystyle 99\degree 17'~52''\)

\(\displaystyle \degree \)\(\displaystyle '\)\(\displaystyle ''\)

 

Решение

На рисунке \(\displaystyle \alpha\) и \(\displaystyle \beta\) – смежные углы.

По свойству смежных углов, сумма их величин равна \(\displaystyle 180\degree{\small .}\)

Если  \(\displaystyle \alpha\) и \(\displaystyle \beta~-\) величины смежных углов и величина \(\displaystyle \alpha\) известна,  то \(\displaystyle \beta = 180\degree-\alpha{\small .}\)

1. \(\displaystyle \alpha=40\degree{\small .}\)

\(\displaystyle \beta=180\degree - 40\degree= 140\degree{\small .}\)

2.\(\displaystyle \alpha=90\degree{\small .}\)

3. \(\displaystyle \alpha=133\degree{\small .}\)

4. \(\displaystyle \alpha=28\degree 35'{\small .}\)

В одном градусе содержится \(\displaystyle 60\) минут:

\(\displaystyle 1\degree=60'{\small .}\)

Поэтому:

\(\displaystyle \beta=180\degree -28\degree 35'=179 \degree+60' -28\degree- 35' =151\degree25'{\small .}\)

5. \(\displaystyle \alpha=99\degree 17'~52''{\small .}\)

Ответ: