The value of the angle [tex]y[/tex] within the quadrilateral [tex]OABC[/tex] inscribed the circle is 142°.
Let suppose that quadrilateral [tex]OABC[/tex] is a parallelogram. Then, the following conditions must be fulfilled:
- [tex]\overline {OA} \cong \overline {BC}[/tex]
- [tex]\overline{AB} \cong \overline{OC}[/tex]
- [tex]\angle AOC \cong \angle ABC[/tex]
In addition, if we have a rhombus we have the additional condition as A, B and C lie on the circle:
[tex]\overline{OA} \cong \overline {AB} \cong \overline {BC} \cong \overline{OC}[/tex] (4)
If we know that [tex]\angle AOC = 142^{\circ}[/tex], then the value of [tex]\angle ABC = y = 142^{\circ}[/tex].
Based on all these finding, we conclude that the value of the angle [tex]y[/tex] within the quadrilateral [tex]OABC[/tex] inscribed the circle is 142°.
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