Question

What is the measure of each intercepted arc for each inscribed angle of a square inscribed in a circle?

Answer 1

Answer:

The measure of the angle of each of the intercepted arc is 180°

Step-by-step explanation:

An intercepted arc is an encased (between chords) portion of the circumference of the circle. The chords that form the intercepted arc meet at a point

An inscribed angle is the angle is an angle formed between two chords that meet at a point called the end point

For the inscribed square, the symmetry has it that the diagonal is the same as the diameter of the circle as the diagonals bisect each other having equal distances on either side to the circumference of the circle.

Given that the angles in the vertices of the square are 90° and the point of intersection of the two chords forming the vertex are at the ends of the diameter of the circle, which passes through the center of the circle, the angle 90° at the vertex is half the angle at the center which is the angle of the intercepted arc

∴ The measure of the angle of each of the intercepted arc = 2× 90 = 180°.