In the given figure, AD bisects ∠ BAC in the ratio 1: 3 and AD = DB. Determine the value of x.

Question

Philoid · Accepted Answer

Let the ratio be y

⸫ ∠DAB = y

⸫ ∠DAC = 3y

⸫ y + 3y + 108° = 180° [Angle on a straight line]

⇒ 4y = 72°

⸫ y = 18°

⸫ ∠DAC = 3y = 54°

∠ABD = 18° [⸪ AD = DB, ΔABD is an isosceles triangle]

In ΔABC,

⇒ x + ∠A + ∠B = 180° [Sum of all angles of a triangle = 180°]

⇒ x = 180° - 72° - 18°

⸫ x = 90°