ABCDEF is a regular hexagon. The bisector of angle BAF intersects DE at X. Let's write the measurement of angle AXD.
Answers
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Step-by-step explanation:
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°.
Pleasse mark my answer as brainliest.
Step-by-step explanation:
Answer
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°