Q16 of 59 Page 195

ABCDEF is a regular hexagon. The bisector of ∠BAF intersect DE at X. Let’s write the measurement ∠AXD.

Let us first draw a figure for the given question.


In the above figure ABCDEF is a regular hexagon.


AX is the angle bisector of ∠ BAF.


Now for a regular hexagon all its interior angles are equal and all its sides are also equal.


Now ∠ XAF = ∠ BAX = � ∠ BAF = � × 120


= 60°


AFEX is a quadrilateral.


So sum of all interior angles of quadrilateral is 360°.


∠ AFE = ∠ FED = 120° [interior angle of a regular hexagon]


∠ XAF + ∠ AFE + ∠ FEX + ∠ EXA = 360°


60 + 120 + 120 + ∠ EXA = 360°


300° + ∠ EXA = 360°


∠ EXA = 360° - 300°


∠ EXA = 60°


∠ AXD + ∠ EXA = 180° [As they form a linear pair]


∠ AXD = 180 - ∠ EXA


= 180 – 60


=120°


Hence ∠ AXD = 120°.


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