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Calculate the value of the two equal angles in a heptagon if the sum of the other five angles is 780 degrees. 2. Find the sum of the interior angles of a decagon. 3. What is a polygon with nine sides

Mathematics

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  1. Step 1: Determine the total sum of interior angles of a heptagon. A heptagon has n=7n=7 sides. The sum of interior angles is given by the formula (n−2)×180∘(n-2) \times 180^\circ. Sum=(7−2)×180∘=5×180∘=900∘\text{Sum} = (7-2) \times 180^\circ = 5 \times 180^\circ = 900^\circ
  1. Find the sum of the remaining two angles.

    The sum of 5 angles is given as $780^\circ$.
    $$
    \text{Sum of remaining 2 angles} = \text{Total sum} - \text{Sum of 5 angles}
    $$
    $$
    \text{Sum of remaining 2 angles} = 900^\circ - 780^\circ = 120^\circ
    $$
    
  2. Calculate the value of each of the two equal angles.

    Since the other two angles are equal, divide their sum by 2.
    $$
    \text{Value of each angle} = \frac{120^\circ}{2} = 60^\circ
    $$
    The value of each of the other two angles is $\boxed{\text{60}^\circ}$.
    

    9. Step 1: Determine the number of sides of a decagon. A decagon has n=10n=10 sides.

  3. Calculate the sum of interior angles of a decagon.

    Using the formula $(n-2) \times 180^\circ$:
    $$
    \text{Sum} = (10-2) \times 180^\circ = 8 \times 180^\circ = 1440^\circ
    $$
    The sum of angles of a decagon equals $\boxed{\text{1440}^\circ}$.
    

    10. A polygon with nine sides is called a nonagon. A polygon with nine sides is called a nonagon\boxed{\text{nonagon}}.

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