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Example Question #11 : How To Find An Angle In A Polygon
Pentagon is regular. If diagonal is drawn, which of the following describes Quadrilateral ?
Possible Answers:
Quadrilateral is a parallelogram but neither a rectangle nor a rhombus.
Quadrilateral is a rhombus but not a rectangle.
Quadrilateral is a rectangle but not a rhombus.
None of the other responses is correct.
Quadrilateral is a trapezoid.
Correct answer:
Quadrilateral is a trapezoid.
Explanation:
The figure described is below.
Each of the angles of the pentagon has measure
is an isosceles triangle, and , so
and
Since
,
and by the parallel postulate,
Quadrilateral has exactly one pair of parallel sides, so it is a trapezoid.
Sumit
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