Question

Six angles of a heptagon measure 136°, 139°, 110°, 110°, 145°, and 129°. What is the measure of the seventh angle?

Answer 1

To find the measure of the seventh angle of the heptagon, we first need to determine the sum of the interior angles of a heptagon. The formula for the sum of the interior angles of a polygon with \( n \) sides is given by:

\[
\text{Sum} = (n - 2) \times 180°
\]

For a heptagon (\( n = 7 \)):

\[
\text{Sum} = (7 - 2) \times 180° = 5 \times 180° = 900°
\]

Next, we will calculate the sum of the given six angles:

\[
136° + 139° + 110° + 110° + 145° + 129°
\]

Calculating the sum step-by-step:

1. \( 136° + 139° = 275° \)
2. \( 275° + 110° = 385° \)
3. \( 385° + 110° = 495° \)
4. \( 495° + 145° = 640° \)
5. \( 640° + 129° = 769° \)

Now, the total of the six angles is \( 769° \).

Now, we can find the measure of the seventh angle by subtracting the sum of the six angles from the total sum of the heptagon's angles:

\[
\text{Measure of the seventh angle} = 900° - 769° = 131°
\]

Thus, the measure of the seventh angle is:

\[
\boxed{131°}
\]