Download Angles of a Polygons SHEET P3

Angles of a Polygons
SHEET P3
A.
1.
Find the sum of the measures of the angles of a decagon? Of a 100-gon?
2. What is the measure of each exterior angle of an equiangular 30-gon?
3. What is the measure of each interior angle of an octagon? Of a 40-gon?
4. If the sum of the measures of the angles of a polygon is 9,360°, how many sides does the polygon have?
5.
If the measure of each exterior angle of an equiangular polygon is 72°, how many sides does the polygon have?
6. If the measure of each angle of an equiangular polygon is 172°, how many sides does the polygon have?
7. The measure of each angle of an equiangular polygon is five times as large as the measure of an exterior
angle of the polygon. What is the name of the polygon?
8. How many sides does a polygon have if the sum of the measures of its angles is eight times as large as the
sum of the measures of its exterior angles?
9. Two angles of a convex octagon are congruent. Each of the other angles has a degree measure triple that
of each of the first two angles. Find the degree measure of the larger angles.
10. Let S be the sum of the interior angles of a polygon P for which each interior angle is 7.5 times the
exterior angle at the same vertex. Find S.
11. If the sum of all the angles except one of a convex polygon is 2190°, then how many sides does the polygon
have?
12. Diagonals
BD and CE of a regular pentagon ABCDE meet at point Q . Find mBQE .
13. a.) How many diagonals does a square have?
b.) How many diagonals does a pentagon have?
c.) How many diagonals does a hexagon have?
d.) Let A be a vertex of a polygon with
A as a vertex?
n sides. How many diagonals of the polygon have
e.) Use your answer to part d to find a formula for the number of diagonals in a polygon with
n sides. Confirm your formula by comparing with your answers to parts a-c.
14. A given polygon has 27 diagonals. How many sides does the polygon have?
15. The number of diagonals in a regular polygon is equal to the number of sides. What is the number of
degrees in the sum of all interior angles of the polygon?
16. In a given octagon, four angles have measure x degrees and two have measure 2x degrees. The other two
angles are right angles. Is the octagon concave or convex?
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Sheet P3 – side 2
17. Find the sum of the angles at the points of the 7-pointed star ABCDEFG shown. Do not assume that the
heptagon in the center is regular.