Question

Вершины треугольника АВС лежат на окружности, угол А = 70˚, угол С = 30˚ .Чему равна градусная мера дуги АС ?(ответ должен быть 160 градусов, нужно решение!)

Answer 1

Градусная мера дуги в два раза больше градусной меры угла B. Угол B= 180 - (70+30)= 80 гр.
дуга равна 80*2=160гр.

Ответ: 160 гр.

Answer 2

Given Information

We are given that the vertices of triangle ABC lie on a circle, and angle A is 70 degrees while angle C is 30 degrees. We need to find the degree measure of arc AC.

Solution

To find the degree measure of arc AC, we need to determine the central angle that subtends the same arc on the circle.

Since the vertices of triangle ABC lie on a circle, the sum of the angles formed by any two points and the center of the circle is equal to 360 degrees.

Let O be the center of the circle. We can draw radii OA, OB, and OC. The sum of angles AOB, BOC, and COA is equal to 360 degrees.

Since angle A is 70 degrees and angle C is 30 degrees, we can find angle B using the equation:

angle B = 360 - angle A - angle C

Substituting the given values, we have:

angle B = 360 - 70 - 30 = 260 degrees

Now, we can find the degree measure of arc AC by doubling angle B:

degree measure of arc AC = 2 * angle B = 2 * 260 = 520 degrees

Therefore, the degree measure of arc AC is 520 degrees.

Conclusion

The degree measure of arc AC, when the vertices of triangle ABC lie on a circle and angle A is 70 degrees while angle C is 30 degrees, is 520 degrees.