A regular polygon is partially obscured by a box. (Dotted lines show t

A regular polygon is partially obscured by a box. (Dotted lines show that polygon is hidden behind the box.). What is the sum of the angles of the polygon?

(1) x°= y°

(2) x°+ y°= 72°

Each angle of Regular polygon is equal.

Statement 1) x°= y° does not give any clue about angle of regular polygon



Insufficient.

Statement 2) x°+ y°= 72°

x°+ y° + 2 Equal Angle of regular polygon = 360

2 Equal Angle of regular polygon = 360 - x°+ y°
= 360-72
= 288
Each Angle of regular polygon = 144

Now we have one angle of regular polygon. We can calculate no of Sides of regular polygon.

Sufficient.

Each angle of N-sided regular polygon = 180 (n-2) / n
144= 180 (n-2) / n

After solving we get n = 10.

IMO Answer is B

Statement 1 would automatically be true if the horizontal-looking lines at the top of the diagram are genuinely parallel (something we're not told in the question). So Statement 1 gives no information about what type of polygon we have.

From Statement 2, we know two angles in the trapezoid-like shape at the top of the picture add to 72, so the other two angles add to 288, since in a quadrilateral the four angles sum to 360. The angles summing to 288 are in the polygon, and if our polygon is regular, each angle is the same, so is 288/2 = 144 degrees. If we know the size of each angle in a regular polygon, we can work out how many sides it has, and thus answer the question. So Statement 2 is sufficient.

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