Question

in fig AB divides ∠DAC in the ratio 1: 3 and AB =DB. Determine the value of x. if angle CAE is 108 degrees
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Answer 1

Answer:

∠BAC

=

3

1

Given

⇒∠DAB=3∠BAC

∴∠BAC+∠DAB=∠DAC=72°

⇒∠BAC+3∠BAC=72°

⇒4∠BAC=72°

⇒∠BAC=

4

72

=18°

∴∠DAB=3×18°=54°

∴∠DAB=∠BDA=54°(AB=DB)

∴∠ABD=180°−(54°+54°)

=180−108°

=72°

No, ∠DBA=72°=∠BAC+x (Exterio angle)

⇒x=72°−18°=54°

solution