Answer:
122°
Step-by-step explanation:
We are supposed to find value of q
Refer the attached figure
Note: Opposite angles of cyclic quadrilateral are supplementary.
Supplementary angles: A pair of angles whose sum is 180°
So, [tex]\angle ABC + \angle CDA = 180 ^{\circ}[/tex] --1
[tex]\angle ABC = 58 ^{\circ}[/tex]
[tex]\angle CDA = y[/tex]
Substitute the values in 1
[tex]58^{\circ} + y = 180 ^{\circ}[/tex]
[tex]y = 180 ^{\circ}-58^{\circ}[/tex]
[tex]y = 122^{\circ}[/tex]
Thus [tex]\angle CDA = y=122^{\circ}[/tex]
Hence the value of q is 122°
