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Polygons – Basic Concepts, Diagonals, and Angles
I.
Modified True or False. Write “a-ha” if the statement is true, otherwise, change the underlined word to make it true.
1. The larger the number of sides of a polygon, the greater the sum of the measures of its
________
interior angles.
2. The sum of the measures of the interior angles of a polygon is always a multiple of 180°.
________
3. There is a polygon wherein the sum of the measures of its interior angle is 320°.
________
4. An interior angle of a polygon and its adjacent exterior angle are complementary.
________
5. The larger the number of sides of a polygon, the greater the sum of the measures of its
________
exterior angles.
6. If the two angles of the triangle measure 35 and 67, the third angle measures 78.
________
7. A convex nonagon has 27 diagonals.
________
8. The perimeter of a regular decagon is 200 cm. Each side measures 20 cm.
________
9. Regular pentagon has an interior angle measuring 108°.
________
10. The measure of the interior angle of a convex polygon is always greater than the measure of
________
its adjacent exterior angle.
II. Answer the following. SHOW YOUR SOLUTION. Strictly, no solution, no points.
1. What is the measurement of the exterior angle of a regular octadecagon? (2 points)
Solution:
2. A regular polygon has an exterior angle measuring 20°. How many sides does it have? (2 points)
Solution:
3. How many diagonals does a dodecagon have? (4 points)
Solution:
4. A regular polygon with an interior angle measuring 156 degrees is called _________. (4 points)
Solution:
5. What is the sum of the interior angles of a heptadecagon? (4 points)
Solution:
6. The sum of the interior angles of a convex polygon is 3060°. Find the number of sides and identify the type of
the polygon.(4 points)
Solution: