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?
90°
80°
75°
85°
the sum of the interior angles of a heptagon is
180(7-2) = 900°
One angle is missing
x + 120+ 150+ 135 +170 +90 +125 = 900
x = 110
The smallest interior angle will cause the largest exterior angle
so largest exterior is 180 - 90 = 90°
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?
To find the measure of the largest exterior angle of a heptagon, you need to know that the sum of the exterior angles of any polygon is always 360 degrees.
Step 1: Find the sum of the given interior angles:
120° + 150° + 135° + 170° + 90° + 125° = 790°
Step 2: Subtract the sum of the interior angles from 360°:
360° - 790° = -430°
Step 3: Since the given sum is negative, there is a mistake or an impossibility in the given measures of the interior angles. Please double-check the values provided.
Therefore, it is not possible to determine the measure of the largest exterior angle with the given measures of the interior angles.
To find the measure of the largest exterior angle of a heptagon, we can use the fact 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. The interior and exterior angles are related as follows: interior angle + exterior angle = 180 degrees.
Since we know six of the interior angles of the heptagon, we can find the seventh interior angle by subtracting the sum of the given interior angles from 180 degrees:
Missing interior angle = 180° - (120° + 150° + 135° + 170° + 90° + 125°)
Missing interior angle = 180° - 790°
Missing interior angle = -610°
Note that we obtained a negative measure for the missing interior angle. This means that there is an error in the given measures of the interior angles and they do not form a valid heptagon.
Given this information, it is not possible to determine the measure of the largest exterior angle.