How many diagonals does a regular convex octagon have?

A. 16
Incorrect. The formula for finding the number of diagonals of a polygon is n(n − 3) 2 .

B. 20
Correct! Five diagonals are drawn for each vortex.

C. 24
Incorrect. The formula for finding the number of diagonals of a polygon is n(n − 3) 2 .

D. 40
Incorrect. Five diagonals are drawn from each vertex but they can only be counted once.

The vertices of a hexagon are (6,4);(8,1);(6,-4);(0,-4);(-5,1);(-1,4).

Which of the following statements is the best description of the hexagon?

A. Convex and irregular
Correct! The hexagon has sides with different lengths and is convex.

B. Convex and regular
Incorrect. The hexagon is convex but the sides have different lengths.

C. Concave and irregular
Incorrect. The hexagon is irregular but not concave.

D. Concave and regular
Incorrect. The hexagon’s sides are different lengths so it is not regular.

An archeologist uncovered a piece of a broken ceramic plate that was originally in the shape of a regular polygon. The measure of the interior angle is 135°. What was the original shape of the plate?

A. Quadrilateral
Incorrect. The interior angle of a Pentagon is 90°.

B. Pentagon
Incorrect. The interior angle of a Pentagon is 108°.

C. Hexagon
Incorrect. The interior angle of a Hexagon is 120°.

D. Octagon
Correct! The interior angle measure of an Octagon is 135°.

Polygon JKLM ≅ PQRS. Which statement must be true?

1. ∠K ≅ ∠Q
   Correct! Corresponding angles of congruent polygons are congruent.
2. ∠K ≅ ∠P
   Incorrect. This would be true only if the polygons were regular.
3. JK = RS
   Incorrect. JK and RS are not corresponding sides.
4. LM = PQ
   Incorrect. LM and PQ are not corresponding sides.