Respuesta :

Answer: the measure of the remaining angle is 146 degrees

Step-by-step explanation:

The formula for finding the sum of the measure of the interior angles in a regular polygon is expressed as (n - 2) × 180.

A heptagon has 7 sides. This means that the sum of the angles in a heptagon is

180(7 - 2) = 180 × 5 = 900 degrees

Let x represent the measure of the remaining angle of the heptagon. If the measures of a heptagon are 127, 152, 112, 123, 135, and 105, it means that

127 + 152 + 112 + 123 + 135 + 105 + x = 900

754 + x = 900

x = 900 - 754

x = 146 degrees

The measure of remaining angle of heptagon is 146 degree.

The sum of the measures of the interior angles of a heptagon is 900º.

Let us consider that remaining angle is x degree.

Given that, the measures of a heptagon are 127, 152, 112, 123, 135, and 105 degrees.

                     [tex]127+152+112+123+135+105+x=900\\\\754+x=900\\\\x=900-754\\\\x=146[/tex]

Thus, the measure of remaining angle is 146 degree.

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