Question

Polygon A B C D E F has 6 sides. Exterior angle A is 62 degrees, exterior angle B is 44 degrees, exterior angle C is 70 degrees, exterior angle D is 60 degrees, and exterior angle E is 43 degrees.
What is the measure of angle AFE?

79°
81°
91°
99°

Answer 1

To find the measure of angle AFE in polygon ABCDEF, we start by determining the sixth exterior angle, which we will denote as exterior angle F.

1. Recall that the sum of all exterior angles of any polygon is always equal to 360 degrees.

2. We have the following exterior angles provided:
- Angle A = 62 degrees
- Angle B = 44 degrees
- Angle C = 70 degrees
- Angle D = 60 degrees
- Angle E = 43 degrees

Let's add them up:

\[
62 + 44 + 70 + 60 + 43 = 279 \text{ degrees}
\]

3. Next, we subtract this total from 360 degrees to find the exterior angle F:

\[
360 - 279 = 81 \text{ degrees}
\]

So, exterior angle F = 81 degrees.

4. Recall that angle AFE is the interior angle at vertex F. The relationship between an exterior angle and its corresponding interior angle is given by:

\[
\text{Interior angle} = 180 - \text{Exterior angle}
\]

5. Thus, we find angle AFE:

\[
\text{Angle AFE} = 180 - 81 = 99 \text{ degrees}
\]

Therefore, the measure of angle AFE is:

\[
\boxed{99°}
\]