Question

Сто­ро­на AC тре­уголь­ни­ка ABC про­хо­дит через центр опи­сан­ной около него окруж­но­сти. Най­ди­те ∠C, если ∠A = 75°. Ответ дайте в гра­ду­сах.

Answer 1

Так как центр окружности, описанной около треугольника, лежит на его стороне, треугольник прямоугольный.
∠В = 90°, ∠А = 75°.
Сумма острых углов прямоугольного треугольника равна 90°.
∠С = 90° - ∠А = 90° - 75° = 15°

Answer 2

Finding ∠C in Triangle ABC

To find ∠C in triangle ABC, we can use the fact that side AC passes through the center of the circumcircle of triangle ABC. Additionally, we are given that ∠A = 75°.

Using this information, we can calculate the measure of ∠C.

Given: - ∠A = 75° - Side AC passes through the center of the circumcircle of triangle ABC

Calculation of ∠C

We can use the relationship between inscribed angles and central angles to find ∠C. The measure of an inscribed angle is half the measure of the central angle subtending the same arc on the circle.

From the given information, we can calculate the measure of ∠C as follows:

∠C = 2 * ∠A = 2 * 75° = 150°

Therefore, the measure of ∠C in triangle ABC is 150 degrees.

This calculation is based on the relationship between inscribed angles and central angles in a circle, where the measure of an inscribed angle is half the measure of the central angle subtending the same arc on the circle.

If you have any further questions or need additional assistance, feel free to ask!