Final answer:
To find the measure of each remaining interior angle of the convex heptagon, we can use the sum of the angles formula, subtract the given angles, and divide by the number of remaining angles.
Step-by-step explanation:
To find the measure of each remaining interior angle of the convex heptagon, we need to use the fact that the sum of all the interior angles of a polygon is given by the formula (n-2) * 180 degrees, where n is the number of sides.
In this case, since we have a heptagon, n = 7.
The sum of all the interior angles of the heptagon is (7 - 2) * 180 = 5 * 180 = 900 degrees.
From the given information, the sum of the four specified angles is 93 + 47 + 126 + 102 = 368 degrees.
Therefore, the sum of the remaining angles is 900 - 368 = 532 degrees.
Since the remaining angles are congruent, we divide the sum of the remaining angles by the number of remaining angles, which is 7 - 4 = 3.
So each remaining interior angle of the convex heptagon measures 532 / 3 = 177.333... degrees (rounded to three decimal places).