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.