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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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- Step 1: Determine the total sum of interior angles of a heptagon. A heptagon has sides. The sum of interior angles is given by the formula .
Find the sum of the remaining two angles.
The sum of 5 angles is given as $780^\circ$. $$ \text{Sum of remaining 2 angles} = \text{Total sum} - \text{Sum of 5 angles} $$ $$ \text{Sum of remaining 2 angles} = 900^\circ - 780^\circ = 120^\circ $$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 sides.
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 .
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