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If a pair of opposite angles of a quadrilateral are supplementary, the quadrilateral is:
a. Parallelogram
b. Rectangle
c. Cyclic
d. Rhombus

Sagot :

sqdancefan

Answer:

  c. Cyclic

Step-by-step explanation:

You want to know what kind of quadrilateral has a pair of opposite angles that are supplementary.

Opposite angles

Opposite angles of a parallelogram, including a rhombus and rectangle, are congruent. They happen to be supplementary in a rectangle, because they are both 90°.

When a quadrilateral is cyclic, its vertices lie on a circle. Opposite angles will be inscribed angles of that circle intercepting arcs that total the full measure of the circle: 360°. The inscribed angles have half the measure of the arcs, so their sum will be 180°. That is, opposite angles of a cyclic quadrilateral are supplementary.

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Additional comment

A rectangle is a cyclic quadrilateral, but not all cyclic quadrilaterals are rectangles.

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