Question

Точка О-центр кола,MN-його хорда. Знайти кут MON,якщо кут OMN дорівнює 50⁰​

Answer 1

Відповідь до завдання на фото.

Answer 2

Finding the Angle MON

To find the angle MON, we can use the properties of a circle and the relationship between a central angle and an inscribed angle.

Given: - Point O is the center of the circle. - MN is a chord of the circle. - The angle OMN is 50 degrees.

We can find the angle MON using the relationship between a central angle and an inscribed angle. The relationship states that an inscribed angle is half the measure of the central angle that subtends the same arc.

Calculation

Let's denote the angle MON as x. Since OMN is given as 50 degrees, we can use the relationship mentioned above to find the measure of angle MON.

According to the relationship: x = 2 * OMN

Substitute the given value: x = 2 * 50 x = 100 degrees

So, the measure of angle MON is 100 degrees.