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A cyclic quadrilateral is also a kite. If one of the angles is 80 degrees, what is the measure of the opposite angle, m?

May 6, 2026Mathematics

ScanSolve AI Answer

Answer

\text{}100^\circ\text{}

3 steps

Here's how to determine the value of $m$ :

Identify the type of quadrilateral.
The diagram shows a quadrilateral inscribed in a circle, which means it is a cyclic quadrilateral. The markings on the sides indicate that it is also a kite, as it has two distinct pairs of equal-length adjacent sides.
Apply the property of cyclic quadrilaterals.
In a cyclic quadrilateral, the sum of opposite angles is $180^\circ$ . The angle $80^\circ$ and the angle $m$ are opposite angles in the cyclic quadrilateral.
Set up the equation and solve for $m$ .
$m + 80^\circ = 180^\circ$ $m = 180^\circ - 80^\circ$ $m = 100^\circ$
The value of $m$ is $\boxed{\text{}100^\circ\text{}}$ .