The measures of 6 of the interior angles of a heptagon are: 120°, 150°, 135°, 170°, 90°, and 125°. What is the measure of the largest exterior angle?
A heptagon has 7 sides.
The sum of exterior angles is 360.
The six given angles have exterior angles equal to:
60,30,45,10,90 and 55 for a total of 290.
The remaining exterior angle is therefore 360-290=70°.
The largest exterior angle is 90°.
To find the measure of the largest exterior angle of a heptagon, we first need to understand that the sum of all the exterior angles of any polygon is always 360 degrees.
In a heptagon, there are seven interior angles and seven corresponding exterior angles. Each exterior angle is formed by extending one side of the heptagon. Since the heptagon has 7 sides, each exterior angle is 360° divided by 7, which is approximately 51.43°.
Now, to find the largest exterior angle, we need to subtract the given interior angles from 180°. This is because each interior angle and its corresponding exterior angle are supplementary angles - they add up to 180°.
Given that the interior angles are 120°, 150°, 135°, 170°, 90°, and 125°, we can find the sum of these angles:
120° + 150° + 135° + 170° + 90° + 125° = 790°
Next, we subtract this sum from the sum of the interior angles of a heptagon, which is 7 * 180° = 1260°:
1260° - 790° = 470°
Therefore, the measure of the largest exterior angle of the heptagon is 470 degrees.