Question

question 1 of 5. select the correct answer from each drop - down menu. amma completes the construction below. is quadrilateral bcde a square? quadrilateral bcde is a square. segment bd is half the length of diameter ce. therefore, the measure of each central angle of quadrilateral bcde are all congruent. the angles of quadrilateral bcde are all 90 45 60 180. so, arcs bc, cd, de, and be each also have that same measure. so, the sides of quadrilateral bcde are all congruent. arc that measures 180 °, so the angles of quadrilateral bcde are all

Explanation:

Step1: Recall circle - related angle property

The sum of central angles in a circle is 360°. In a square inscribed in a circle, the four central angles corresponding to the four arcs between the vertices of the square are equal.

Step2: Calculate the measure of each central angle

Let the measure of each central angle be \(x\). Since there are 4 central angles and their sum is 360°, we have the equation \(4x = 360\). Solving for \(x\), we get \(x=\frac{360}{4}=90\).

Step3: Recall angle - measure in a square

In a square, all interior angles are 90°. The arcs subtended by the sides of the square at the center of the circle are such that the angles of the square are inscribed angles. The measure of an inscribed angle is half of the measure of the central angle subtended by the same arc. Since the central angle corresponding to each side of the square is 90°, the arcs BC, CD, DE, and BE each measure 90°. And the angles of the square (interior angles of quadrilateral BCDE) are all 90°.

Answer:

The measure of each central angle is 90. The angles of quadrilateral BCDE are all 90.