Предмет: Геометрия, автор: travokurovurij

В окружности с центром О отрезки АС и BD - диаметры. Центральный угол AOD равен 138°. Найдите вписанный угол АСВ. Ответ дайте в градусах.

Приложения:

travokurovurij: Смеж­ные углы BOA и AOD об­ра­зу­ют развёрну­тый угол, по­это­му их сумма равна 180°, от­ку­да ∠AOB = 180° − 138° = 42°. Угол AOB — цен­траль­ный, сле­до­ва­тель­но, он равен дуге, на ко­то­рую опи­ра­ет­ся, угол ACB — впи­сан­ный, сле­до­ва­тель­но, он равен по­ло­ви­не дуги, на ко­то­рую опи­ра­ет­ся. По­сколь­ку углы AOB и ACB опи­ра­ют­ся на одну и ту же дугу, угол ACB равен по­ло­ви­не угла AOB, то есть 21°.

Ответы

Автор ответа: someone131313
1

Ответ:

Смеж­ные углы BOA и AOD об­ра­зу­ют развёрну­тый угол, по­это­му их сумма равна 180°, от­ку­да ∠AOB = 180° − 138° = 42°. Угол AOB — цен­траль­ный, сле­до­ва­тель­но, он равен дуге, на ко­то­рую опи­ра­ет­ся, угол ACB — впи­сан­ный, сле­до­ва­тель­но, он равен по­ло­ви­не дуги, на ко­то­рую опи­ра­ет­ся. По­сколь­ку углы AOB и ACB опи­ра­ют­ся на одну и ту же дугу, угол ACB равен по­ло­ви­не угла AOB, то есть 21°.

Объяснение:

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