A picture frame is shaped as a heptagon. The measure of one angle is 126°. The remaining interior angles are congruent. What is the measure of each remaining interior angle in the picture frame?
how many degrees in a heptagon? is it 360? because of that's correct, here how to work it out:
a= single angle
126+6a=360
6a=234
a=39
hope that helps!
The sum of the angles in an n-gon is 180(n-3)
3-gon = 180 (triangle)
4-gon = 360 (rectangle)
...
For a heptagon, that's 5(180) = 900
126+6a = 900
6a = 774
a = 129
That makes more sense. Try drawing a 7-sided figure with one large obtuse angle, and all the rest these bitty 39-degree angles!
129°
To solve this problem, we can start by determining the sum of the interior angles of a heptagon.
A heptagon has seven sides, so it also has seven interior angles. The formula to determine the sum of the interior angles of a heptagon is (n - 2) * 180°, where n is the number of sides. In this case, n = 7, so the sum of the interior angles is (7 - 2) * 180° = 5 * 180° = 900°.
We know that one angle measures 126°, so we can subtract this angle from the sum of the interior angles to find the combined measure of the remaining interior angles.
Remaining interior angles = Sum of interior angles - Given angle
Remaining interior angles = 900° - 126°
Remaining interior angles = 774°
Since there are six congruent interior angles left, we can find the measure of each angle by dividing the combined measure of the remaining interior angles by the number of angles.
Measure of each remaining interior angle = Remaining interior angles / Number of angles
Measure of each remaining interior angle = 774° / 6
Measure of each remaining interior angle = 129°
Therefore, each remaining interior angle in the picture frame measures 129°.