ABCDEF IS A REGULAR HEXAGON . FIND EACH ANGLE OF TRIANGLE ABE
Answers
Answered by
4
AB = CB (sides of regular hexagon ABCDEF)
AF = CD (sides of regular hexagon ABCDEF)
∠BAF = ∠BCD (angle of regular hexagon ABCDEF)
∴∆ABF ≅ ∆CBD (SAS congruency)
⇒ BF = BD (CPCT) ... (6)
And ∠ABF = ∠CBD
⇒ ∠CBD = 30° ... (7)
In ∆BEF and ∆BED
EF = ED (sides of regular hexagon ABCDEF)
BF = BD [from (6)]
BE = BE (common)
∴∆BEF ≅ ∆BED (SSS congruency)
By CPCT
∠EBF = ∠EBD ... (8)
Now ∠ABC = 120° [using (1)]
⇒∠ABF + ∠EBF + ∠EBD + ∠CBD = 120°
⇒ 30° + ∠EBF + ∠EBF + 30° = 120° [using (3), (6), (7) and (8)]
⇒ 2∠EBF = 120° – 60° = 60°
⇒ ∠EBF = 30°
Now using angle sum property for ∆EBF
∠EBF + ∠BFE + ∠BEF = 180°
⇒30° + 90° + ∠BEF = 180°
∠BEF = 180° – 120° = 60°
Similar questions