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Quadrilateral
is cyclic because the sum of its opposite angles equals
.
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Mind Expander
To show that quadrilateral
is cyclic, we need to establish that opposite angles sum to
.
-
From the statement
, we know that angle and angle relate in such a way that they are equal, which is an important condition for cyclic quadrilaterals. -
Next, we refer to the fact that
. This implies that angles and are supplementary due to corresponding properties of cyclic quadrilaterals where angles opposite each other must sum to . -
Finally, with
bisecting , we can conclude that confirms the relationship between all angles in correspondence to a cyclic quadrilateral’s properties.
Thus, quadrilateral
is cyclic if the above conditions are satisfied with the angles appropriately summing to
.