Question

question 3 of 5
type the correct answer in each box. use numerals instead of words. if necessary, use / for the fraction bar.
a square is constructed in circle o. what are the measures of the angles and arcs?
m $overset{\frown}{ay}$=

m $overset{\frown}{ab}$=

m$\angle$aox =

Explanation:

Step1: Recall circle - arc properties

A full - circle has 360°. Since a square is inscribed in the circle, the circle is divided into 4 equal arcs by the vertices of the square.

Step2: Calculate measure of arc AY

The circle is divided into 4 equal arcs by the vertices of the square. So, \(m\overset{\frown}{AY}=\frac{360^{\circ}}{4}=90^{\circ}\).

Step3: Calculate measure of arc AB

Similarly, \(m\overset{\frown}{AB}=\frac{360^{\circ}}{4}=90^{\circ}\).

Step4: Recall central - angle properties

The central angle is equal to the measure of the arc it subtends. Since \(m\overset{\frown}{AX} = 90^{\circ}\), and \(\angle AOX\) is the central angle corresponding to arc \(\overset{\frown}{AX}\), \(m\angle AOX = 90^{\circ}\).

Answer:

\(m\overset{\frown}{AY}=90\)
\(m\overset{\frown}{AB}=90\)
\(m\angle AOX = 90\)