In figure, AB divides ∠DAC in the ratio 1 : 3 and AB = DB. Determine

1.	In figure, AB divides ∠DAC in the ratio 1 : 3 and AB = DB. Determine the value of x.
Answer» Let ∠BAD = y, ∠BAC = 3y ∠BDA = ∠BAD = y (As AB = DB) Now, ∠BAD + ∠BAC + 108° = 180° [Linear Pair] y + 3y + 108° = 180° 4y = 72° or y = 18° Now, In ΔADC ∠ADC + ∠ACD = 108° [Exterior Angle Property] x + 18° = 180° x = 90°

In figure, AB divides ∠DAC in the ratio 1 : 3 and AB = DB. Determine the value of x.

Answer»

Let ∠BAD = y, ∠BAC = 3y

∠BDA = ∠BAD = y (As AB = DB)

Now, ∠BAD + ∠BAC + 108° = 180° [Linear Pair]

y + 3y + 108° = 180°

4y = 72°

or y = 18°

Now, In ΔADC

∠ADC + ∠ACD = 108° [Exterior Angle Property]

x + 18° = 180°

x = 90°