The measure of the interior angle adjacent to the seventh exterior angle is 87°
Step-by-step explanation:
In the n-side polygon
∵ A heptagon has 6 exterior angles with measures of 47, 55,
62, 64, 54, and 49
∵ The sum of the measures of the exterior angles of any
polygon is 360°
∵ The heptagon has 7 angles
∴ 47 + 55 + 62 + 54 + 49 + 7th angle = 360
∵ 47 + 55 + 62 + 54 + 49 = 267
∴ 267 + 7th angle = 360
- Subtract 267 from both sides
∴ 7th angle = 93°
∴ The measure of the 7th exterior angle is 93°
∵ The sum of the measures of the interior angle and the exterior
angle at one vertex is 180°
∴ The 7th interior angle + the 7th exterior angle = 180°
∵ The measure of the 7th exterior angle is 93°
∴ The 7th interior angle + 93 = 180
- Subtract 93 from both sides
∴ The 7th interior angle = 87°
The measure of the interior angle adjacent to the seventh exterior angle is 87°
Learn more:
You can learn more about the polygon in brainly.com/question/6281564
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