Question

1. Центральний кут у колі дорівнює 160°. Тоді градусна міра відповідного Вписаного кута становить:​

Answer 1

Ответ:

40 градусів бісектриса а 50 градусів верхній кут

Answer 2

Calculation of the Inscribed Angle

To find the measure of the inscribed angle corresponding to a central angle, we can use the relationship between the central angle and the inscribed angle in a circle.

In a circle, the measure of the central angle is twice the measure of the inscribed angle that intercepts the same arc. This relationship is known as the Inscribed Angle Theorem.

Given that the central angle measures 160°, we can find the measure of the corresponding inscribed angle by dividing the central angle measure by 2.

Therefore, the measure of the inscribed angle is 80°.

Explanation

Let's break down the problem step by step:

1. The central angle in a circle is the angle formed by two radii that intercept an arc on the circumference of the circle. 2. The inscribed angle is the angle formed by two chords that intersect on the circumference of the circle. 3. The Inscribed Angle Theorem states that the measure of the inscribed angle is half the measure of the central angle that intercepts the same arc.

In this case, the central angle measures 160°. By applying the Inscribed Angle Theorem, we divide the central angle measure by 2 to find the measure of the inscribed angle. Therefore, the inscribed angle measures 80°.

Conclusion

The measure of the inscribed angle corresponding to a central angle of 160° is 80°.