# The central angle AOB is 30 degrees greater than the angle inscribed in the circle and resting

March 25, 2021 | education

| **The central angle AOB is 30 degrees greater than the angle inscribed in the circle and resting on the arc AB. Find the values of these angles.**

Let the value of the central angle AOB be equal to X0, and the value of the inscribed angle ACB equal to Y0.

Then, by hypothesis, X – Y = 30. (1).

Since the value of the inscribed angle is equal to half the value of the central angle, then:

2 * Y = X. (2).

Let us solve the system of two equations 1 and 2 by the substitution method.

2 * Y – Y = 30.

Y = ASB = 30.

X = AOB = Y + 30 = 30 + 30 = 60.

Answer: The center angle is 60, the inscribed angle is 30.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.