02754120
Solving Statement Problems Using Polygon Interior Angle Sum
Theorem
Alert! The key to solving statement problems involving Polygon
Interior Angles Sum Conjecture is to translate English phrases/sentences
into mathematical expressions/equations.
Algebraic Expressions (Chart)
Sum of interior Measure of
 Measures
each (“one”/”
an”)  if
regular/equiangular
(n-2) 180,
where n is the
number of
sides
(n-2) 180
n
where n is the
number of
sides
Algebraic Equations: (How many sides?)
How many sides….if
How many sides does
the sum of the
a regular/equiangular
interior angles
polygon have if each
measure ___?
angle measures
____?
(n-2) 180 = ______,
where n is the
number of sides
(n-2) 180 =_______
n
where n is the
number of sides
Examples
a. What is the sum of the interior angle measures of a decagon?
b. What is the measure of each angle of a regular decagon?
c. ( How many sides) does a polygon have if the sum of the interior angles measure
1,440?
d. (How many sides) does a regular polygon have if each angle measures 144?
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02754120
NAME _____________ PD_____ DATE_________
POLYGON INTERIOR ANGLES SUM
P-H TEXT: ________________________________
DIRECTIONS:
1. Underline key phrases/sentences.
2. Translate words to symbols.
3. Evaluate the expression or solve the equation.
4. Show ALL work on a separate sheet of paper.
1. What is the sum of the measures of the angles of a decagon?
2. What is the sum of the measures of the angles of a 25-gon?
3. How many sides does a polygon have if the sum of the angle measures is
2700?
4. What is the measure of each angle of an equiangular polygon?
5. What is the measure of each angle of a regular hexagon?
6. How many sides does an equiangular polygon have if each angle measures
170?
7. How many sides does an equiangular polygon have if each angle measures
174?
8. Archaeologist Ertha Diggs has uncovered a piece of ceramic plate. The
original plate appears to have been in the shape of a regular polygon. If the
original plate was a regular 16-gon, it was probably a ceremonial dish from
the 3rd Century Ho Ping dynasty. If it was a regular 18-gon, it was probably
a palace dinner plate from the 12th century Wai Ting Dynasty. Ertha
measures each of the sides of her pieces and finds they are all the same
size. She conjectures that all the sides of the original whole plate were the
same size. She measures each of the angles on the piece and finds they are
all the same size. She conjectures that all the angles of the original whole
plate were equal. If each angle measures 160, what dynasty did the plate
come from?
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