# Sum of degree - SOLVED:The sum of the measures of two angles is 183.6°. One angle has a measure of 54°. What is m , the measure in degrees of the second angle?

## Sum of Interior Angles of a Polygon

Remember that the three interior angles of a triangle have a sum of 180 degrees.

• Pentagon Angles The word polygon comes from a Greek word meaning many angles.

• When we use this in the formula, we have: ° ° ° ° Now, if we consider a hexagon, which has six sides, we have: ° ° ° ° The following is a table with the sum of the interior angles of the most common polygons: Polygon Number of sides Sum of angles Triangle 3 180° Quadrilateral 4 360° Pentagon 5 540° Hexagon 6 720° Heptagon 7 900° Octagon 8 1080° Nonagon 9 1260° Decagon 10 1440° Internal angles of a regular polygon We can determine the measure of each of the interior angles of a regular polygon starting from the sum of all the interior angles.

## combinatorial optimization

A regular pentagon has five equal sides and five equal interior angles.

• We know that a regular polygon has all its sides with the same length and all its angles with the same measure.

• To put it another way, a polygon is a two-dimensional closed shape with at least three straight sides and three angles.

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