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:
- \( 136° + 139° = 275° \)
- \( 275° + 110° = 385° \)
- \( 385° + 110° = 495° \)
- \( 495° + 145° = 640° \)
- \( 640° + 129° = 769° \)
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:
\[ \boxed{131°} \]
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