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Two of the interior angles of a polygon are 156 degrees and 134 degrees. Each of the remaining angles is 151 degrees. How many sides does the polygon have?

a) 6

b) 7

c) 8

d) 9

1 Answer

4 votes

Final answer:

To find the number of sides of the polygon, use the formula for the sum of the interior angles of a polygon. Simplify the equation and solve for n. The polygon has 6 sides.

Step-by-step explanation:

To find the number of sides of the polygon, we need to use the formula for the sum of the interior angles of a polygon. The formula is:

Sum of interior angles = (n - 2) * 180° where n is the number of sides.

Given that two angles are 156° and 134°, and the remaining angles are 151°, we can set up the equation:

156° + 134° + (n-4) * 151° = (n-2) * 180°

Simplifying the equation, we get:

290° + (n-4) * 151° = (n-2) * 180°

Expanding and rearranging the equation, we get:

290° - 151° * 4 + 151° * n = 180° * n - 360°

Combining like terms, we get:

151° * n - 604° + 290° + 360° = 180° * n

Simplifying further, we get:

-354° + 360° = 29° * n

6° = 29° * n

Dividing both sides by 29°, we get:

6 = n

Therefore, the polygon has 6 sides. The correct answer is (a) 6.

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