If 5 angles of a heptagon have measures of 80 degrees, 85 degrees, 175 degrees, 90 degrees, and 140 degrees, and if the other two angles are congruent, what is the measure of each of the two other angles? ( "hepta" means seven )

Question

aum · Answer

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What is the sum of all the interior angles of a heptagon? You can memorize the formula and use it or you can figure it out as follows: Choose a point "O" inside the heptagon (if you'd prefer it can be near the center of the heptagon). Join "O" to each of the seven vertices of the heptagon. How many triangles will be formed?  What will be the sum of all the angles of all these triangles?  Subtract from this sum the total of all the angles formed at "O" to derive the sum of all internal angles of the heptagon.

anonymous · Answer

I really need help @aum

aum · Answer

The sum of the three angles in a triangle is 180 degrees.  
In the diagram above, 7 triangles are formed.  
The sum of all angles in 7 triangles = 180 * 7 = 1260 degrees.  
The sum of all angles formed at "O" is: 360 degrees.
Therefore, the sum of all the internal angles of the heptagon = 1260 - 360 = 900 degrees.
Add all the internal angles provided in the problem.
80 + 85 + 175 + 90 + 140 + x + x = 900

Solve for x.

anonymous · Answer

ok thanx @aum