PSAT Math : How to find an angle in a polygon

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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Example Question #106 : Plane Geometry

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.

None of the other responses is correct.

Quadrilateral  is a trapezoid.

Quadrilateral  is a rectangle but not a rhombus.

Correct answer:

Quadrilateral  is a trapezoid.

Explanation:

The figure described is below.

Pentagon

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. 

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