[quote="franteraoka"]A polygon is regular if all the sides are equal and all the interior angles are equal. Two sides of regular octagon O lie on lines l and m, respectively. If l and m intersect, what is the angle of intersection as measured

facing in toward the octagon?

(1) Lines l and m do not intersect at a vertex of O

(2) A line bisecting the angle of intersection of l and m also bisects an interior angle of O.

Please refer the affixed diagram.

There are 3 cases when two sides of the regular octagon lies on the line l and m and they intersect each other.

Case-11 and 2 intersect, they make a right angle out side the octagon.

Case-24 and 5 intersect, they make an obtuse angle at the interior of the octagon.

Case-36 and 1 intersect, they make an acute angle at the out side the octagon.

N.B:- All intersecting angles are considered facing towards the octagon as per given condition.

Question stem:- Measure of angle of intersection=?

Statement-1:- Lines l and m do not intersect at a vertex of O

Case-2 is eliminated since the lines meet at vertex "E".

Case-1 & 3 are valid. So, we have more than one measure of required angle.

Hence, insufficient.

Statement-2:- A line bisecting the angle of intersection of l and m also bisects an interior angle of O.

Case-1 is eliminated since the line bisecting the angle of intersection of 'l' and 'm' doesn't bisect the interior angle of octagon rather bisects the pair of opposite sides.

Case-2 & 3 are valid. So, we have more than one measure of required angle.

Hence, insufficient.

Combining st1 & st2, we have , only case-3 ,which is valid in both the circumstances.

Hence, we have one measure of angle of intersection.

Therefore sufficient.

Ans. (C)

Attachments

Octagon.JPG [ 38.43 KiB | Viewed 321 times ]

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Regards,

PKN

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