Question

Отрезки АС и ВD диаметры окружности с центром О. Угол АСВ равен 16°. найдите угол АОD. ответ дайте в градусах

Answer 1

Решение находится на фото!)

Answer 2

Problem Analysis

We are given that AC and BD are chords of a circle with center O. The angle ACB is 16°. We need to find the angle AOD.

Solution

To find the angle AOD, we can use the following steps:

1. Since AC and BD are chords of the same circle, we can use the inscribed angle theorem, which states that the measure of an inscribed angle is half the measure of its intercepted arc. 2. The angle ACB is given as 16°. Therefore, the intercepted arc AB has a measure of 2 * 16° = 32°. 3. Since the angle AOD is an inscribed angle that intercepts the same arc AB, its measure is also 32°.

Therefore, the angle AOD is 32°.

Answer

The angle AOD is 32°.